In this technical note, we are concerned with constrained consensus algorithms for distributed convex optimization with a sum of convex objective functions subject to local bound and equality constraints. In multiagent networks, each agent has its own data on objective function and constraints. All the agents cooperatively find the minimizer, while each agent can only communicate with its neighbors. The consensus of multiagent networks with time-invariant and undirected graphs is proven by the Lyapunov method. Compared with existing consensus algorithms for distributed optimization with diminishing step sizes, the proposed algorithms with fixed step size have better convergence rate. Simulation results on a numerical example are presented to substantiate the performance and characteristics of the proposed algorithms.