We study the problem of resilient consensus in multi-agent networks with bounded input constraints. The resilient update rules takes account of the presence of attacks by malicious agents in the network. Each regular agent solves a constrained finite-time optimal problem with the states of its neighbors and updates its state based on a predetermined update rule. A scheme is proposed to solve the problem with synchronous communication, assuming that the maximum number of malicious nodes is known. We derive an algorithm which ignores the large and small value from neighbors to avoid the influence of malicious nodes. It is guaranteed to attain resilient consensus under the topological condition expressed in terms of graph robustness. Simulation examples are provided to demonstrate the effectiveness of the proposed algorithm.