This paper considers the problem of selecting the top-m designs using simulation with input uncertainty. The performance of each design is measured by its worst case performance. The objective of this paper is to maximize the probability of correctly selecting the top-m designs given a fixed simulation budget. Due to the complexity of probability of correct selection (PCS), we develop a lower bound for the PCS and derive an asymptotically optimal budget allocation rule. Useful insights on characterizing the efficient budget allocation rule with input uncertainty are provided. Meanwhile, a sequential simulation procedure is suggested to implement the allocation rule. A series of numerical experiments indicate that the proposed simulation budget allocation rule can outperform all existing selection rules.