@annav is correct, of course, but I think maybe missing the op's intuitive reasoning that's suggesting "no force" to him:
(a) Suppose you're sitting in an accelerating automobile. Then you >>feel<< a force that's responsible for accelerating you forwards.
(b) But suppose instead you're in free fall, in a gravitational field, accelerating downwards. Then you feel absolutely nothing, no force whatsoever. So, yes, there must be a force, but >>where is it???<<, so to speak.
Answer: (a) You feel a force while sitting in an accelerating car because the force acts directly on your back, but not directly on the rest of your body. The carseat presses your back, then your back presses on your internal organs, etc. And it's all this pressing of one part of your body on another part that you're feeling. (This is called a contact force -- one object pushing on another that it's in contact with.)
(b) But in a gravitational field, gravity acts >>directly on every part<< of your body simultaneously. Even on every cell, every molecule, of every internal organ. So no one part of your body is pressing against any other part. All your "parts" are moving together, in unison, so to speak. And so you >>feel nothing<< directly. But there nevertheless is an overall force, gravity, just like everybody else already explained. (And note that gravity is not a contact force -- it acts at a distance, without being in contact with the objects it's acting on. And that's why it can directly affect your internal organs, which the accelerating car can't do.)
Note that prior to Newton's discovery/explanation of gravity, everybody believed that all forces were contact forces. Nobody ever imagined that one body could exert a force on another body without being directly in contact with it. And at first blush, that indeed sounds pretty reasonable. So Newton's genius was not only explaining gravity, but also conjuring up the almost unimaginable idea of force-at-a-distance in the first place.
So your intuition is quite understandable -- you don't feel a force, so how can there possibly be a force??? Action(force)-at-a-distance is the answer. But don't feel too bad -- it took Isaac Newton to figure that out.