Yes, an object can have zero velocity and still be accelerating simultaneously.
Let us consider an object moving in the forward direction. Now, suddenly a force acts on it and tries to accelerate the object in the reversed direction. While observing the object, you will find that the object will continue to move forward for some time and then stops instantly. Then the object will start to move in the backward direction.
When the body is projected vertically up, at the highest point its speed becomes zero whereas it is accelerating downwards with g = 9.8 m/s2.