History of the Milky Way-Quasar Was our Milky Way a Quasar many years ago? I heard that it is difficult to fuel quasars for many billions of years, after a quasar finishes accreting the surrounding gas and dust, it becomes an ordinary galaxy. 
 A: It's possible, because, as you said,  a quasar is a supermassive black hole (SMBH) that is accreting matter & spewing out a huge jet of material. All we need is a bit of evidence showing that our SMBH had jets and we might be able to convince ourselves that it is true.
It turns out that in 2013, the Chandra Telescope and VLA did some combined research and found that Sgr A* did actually have a jet. As far as I know, this hasn't been cited as clear evidence that the MW galaxy hosted a quasar, but it does suggest that Sgr A* was pretty active a long time ago.  There are also the so-called Fermi bubbles that suggest a strong outflow from the center of the galaxy. The Chandra+VLA paper, Li, Morris, Baganoff (2013) (arXiv link), cite the "Fermi Bubble" paper, Su, Slatyer & Finkbeiner (2010) (also arXiv link), saying only (link my addition)

Interestingly, the Fermi bubbles (Su, Slatyer & Finkbeiner 2010) have been suggested to be created by bi-polar jets following the Galaxy’s rotation axis (Guo & Mathews 2012)

before moving on to describing the jet energetics.
The next question, of course, is "Could Sgr A* become a quasar in the future?" This was discussed over at Universe Today earlier in the year,

Since the Milky Way is already a middle aged galaxy, its quasaring days are probably long over. However, there’s an upcoming event that might cause it to flare up again. In about 4 billion years, Andromeda is going to cuddle with the Milky Way, disrupting the cores of both galaxies. During this colossal event, the supermassive black holes in our two galaxies will interact, messing with the orbits of stars, planets, gas and dust.
Some will be thrown out into space, while others will be torn apart and fed to the black holes. And if enough material piles up, maybe our Milky Way will become a quasar after all.

So there's a possibility it could in the future, as it possibly did in the past.
