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Yes it may have. Acceleration is the rate of change of velocity and not speed.Velocity is speed with direction attached to it. So even if the magnitude of velocity (speed) remains constant the direction may change and so the body will have an acceleration.

Example - A body moving on a circular track with uniform speed has a acceleration of  \frac{mv^2}{r} , though it has a constant speed. The reason is that the direction of speed is changing (the direction is given by the tangent to the circular path)