This paper considers a class of distributed convex optimization problems with constraints and gives a novel multi-agent neurodynamic approach in continuous-time form. The considered distributed optimization is to search for a minimizer of the summation of nonsmooth convex functions on some agents, which are with local general constraints. The proposed approach solves the objective function of each agent individually, and the state solutions of all agents reach consensus asymptotically under mild assumptions. In particular, the existence and boundedness of global state solution to the dynamical system are guaranteed. Moreover, the state solution reaches the feasible region of equivalent optimization problem asymptotically and the output of each agent is convergent to the optimal solution set of primal distributed problem. Contrasting to the existing methods in distributed manner, the proposed approach is more convenient for general constrained distributed problems and has low structure complexity which could narrow the bandwidth of communication. Finally, the proposed neurodynamic approach is applied to two numerical examples and a class of power system optimal load sharing problems to support the theoretically results and its efficiency.