This paper investigates resilient consensus problems over directed networks with state constraints. Cooperative agents in the network can potentially be influenced by uncooperative neighbors, who are knowledgeable, anonymous and able to spread misinformation. We formulate the resilient constrained consensus problem for high-dimensional multi-agent systems. A projection based resilient constrained consensus protocol is presented so that the agent’s state will be pushed back to the constraint set when it approaches the boundary. We show that resilient constrained consensus can be reached for robust networks when the constraint sets are convex and share a non-empty overlap. The proposed algorithm is of low complexity, purely distributed, and can be performed in tandem with a max-consensus process to estimate the allowed number of uncooperative neighbors.