In this letter, we study the consensus-based leader-follower algorithm in mobile sensor networks, where the goal for the entire network is to converge to the state of a leader. We capture the mobility in the leader-follower algorithm by abstracting it as a Linear Time-Varying (LTV) system with random system matrices. In particular, a mobile node, moving randomly in a bounded region, updates its state when it finds neighbors; and does not update when it is not in the communication range of any other node. In this context, we develop certain regularity conditions on the system and input matrices such that each follower converges to the leader state. To analyze the corresponding LTV system, we partition the entire chain of system matrices into non-overlapping slices, and relate the convergence of the sensor network to the lengths of these slices. In contrast to the existing results, we show that a bounded length on the slices, capturing the dissemination of information from the leader to the followers, is not required; as long as the slice-lengths are finite and do not grow faster than a certain exponential rate.