You are right, the velocity of the object is changing since it's a projectile - BUT we're talking about velocity in the x-direction. That will remain constant until the projectile hits the ground. Velocity in the y-direction, however, will change (since gravity makes things accelerate).
Imagine you are in space and you throw something in a straight line. Does it speed up or slow down? No, it remains at a constant velocity (as long as air resistance is discounted).
The same holds for a projectile thrown/fired on earth. The only difference is that it stops when it hits the ground - which happens because there's gravity on earth to pull it down. As long as air resistance is not counted, projectiles will continue at a constant velocity in the direction that is perpendicular to gravity (i.e. along the x-axis) until some other force acts on them.
Here's an example I found useful: a bullet fired from a gun (that is aiming perpendicular to the ground) and a bullet dropped from the same height will hit the ground at the same time.
