This paper studies constrained consensus for continuous-time multiagent systems, where agents are subject to different state constraints. A projection-based consensus protocol is presented where a projection operator is used on top of the traditional consensus protocol in order to keep the state staying inside the constraint set. This operator can ensure the smoothness of the state trajectory under projection and it will only be used when the state is close to the boundary of the constraint set and about to move outside. Under this protocol, each individual agent only needs to know its own state and constraint set as well as the relative states to its neighboring agents. With the assumption that all constraint sets are convex and have nonempty intersection, it is proven that global consensus can be achieved without violating any state constraints during the transience.