The average velocity of a body can be zero, but average speed of a body cannot be zero.

 Speed indicates only the rate of change of position with time, it does not indicate the direction of change of position. The velocity states the rate of change of position along with its direction that is, velocity means the rate of change of position in a definite direction or in other words the rate of change of displacement. The average velocity depends on the net displacement of a body so if a body starts from a position and comes back to the same position after some time, the net displacement is zero. Consequently, the average velocity is zero. While the speed depends on the actual path length covered. It can't be zero if a body has displaced from its position. 


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