Any tracking algorithm must be able to detect interested moving objects in its field of view and then track it from frame to frame. The tracking algorithms based on mean shift are robust and efficient. But they have limitations like inaccuracy of target localization, object being tracked must not pass by another object with similar features i.e. occlusion and fast object motion. This paper proposes and compares an improved adaptive mean shift algorithm and adaptive mean shift using a convex kernel function through motion information. Experimental results show that both methods track the object without tracking errors. Adaptive method gives less computation cost and proper target localization and Mean shift using convex kernel function shows good results for the tracking challenges like partial occlusion and fast object motion faced by basic Mean shift algorithm.