Would we require energy to walk in a gravity free space? If there was no gravity would our leg muscles lose energy to make us walk.
When we walk we cover strides . when we lift our one leg from rest on ground accelerate it until it reaches top say to speed v which is equal to speed of walking ( constant ) and then decelerate it to rest again when our foot touches the ground this completes one stride.
For the other leg one stride is similar when one leg is at rest on ground other is at top with constant speed v. Here we ignore work done on lifing foot against gravity.
So if there were no gravity would we need energy to walk ?
 A: Would we require energy to walk in a gravity free space?
This can't be answered since walking requires gravity, at least the motion most people would understand as "walking".
Think about how walking works.  Feet pressed on the ground push laterally against the ground to move us forward.  Eventually a foot gets extended so far behind the body that it can't usefully push laterally anymore.  That foot is then lifted, moved forward, pressed against the ground again, and the cycle repeats.
Without gravity, there is no way to push down on the ground and remain in contact with the ground for long.  Pushing down will accelerate you upwards.  You then soon move upwards far enough so that you can't reach the ground anymore.  No more walking.
Even if the feet could magically stay in contact with the ground, without a vertical force there is no friction to support the lateral forces that are the essence of walking.  If you assume some system, like magnetic boots for example, to keep the feet pressed against the ground, then you have to specify that.
Again, the question make no sense.
A: In a gravity-free space, one does not walk. You can see, for example, astronauts at the International Space Station doing their thing; it's a lot of "pushing off of walls" etc. to get to where you want to go. You still need energy to push off of walls and to stop, but during the middle you're pretty much flying without resistance -- wind resistance at low speeds is not very much.
Another tool to help in thinking about issues related to walking is a bicycle on a good road. We have a lot of clumsy intuitions about motion which come from the fact that walking is this very clumsy action of maintaining constant balance while sequentially falling over and over again onto your other foot, so we conflate energies to contract muscles with forces with stresses with damage/pain/sensation in complicated ways.
A lot of this can be mitigated by understanding a bicycle on a good road, you have to pedal hard to get up to speed, then at-speed you can just "coast", then you have to expend a lot of energy into the brakes in order to slow down. 
You can actually "unpedal" this on some bikes which have a "fixed gear" setup but they are less popular. Basically in fixed gear bikes you do not "coast" in the same way: your legs are always moving forward in a circle as long as you are moving forward. But when you "coast" the pedals just kind of "drag your feet along for the ride" and when you accelerate you push in the way that the pedals are going and when you decelerate you have to "fight" the pedals by pushing the reverse way.
Anyway, the point is that the energy cost of walking is not part of this "we accelerate and decelerate our legs" issue, it's part of the "we decelerate our legs by crashing them into the ground" issue that does not provide us a good way to recoup that energy. This is also why humans can run 20-25 km/hr with jumping stilts on, even though if you ever see people running with jumping stilts, you will think "you were not evolved to run that way..."
A: 
If there was no gravity would our leg muscles lose energy to make us walk.

Well apart from there being no way to walk (as already discussed by others) your muscles, if unused or underused, will start to atrophy and you'll loose muscle.  This affects more than just your legs, like your heart.

So if there were no gravity would we need energy to walk ?

You can't walk, but you still need energy to change position, orientation and even to breath.
You will need to do equivalent exercise simply to maintain muscle and general health.
