This paper studies a class of multi-agent optimization problems with coupled equality and inequality constraints, where the objective function is the sum of local functions known only by local agent itself. In addition, the local objective functions and constraint function in the problem are convex, not necessarily smooth, nor necessarily strongly convex or strictly convex. Compared with optimization problems with non-coupled inequality constraints, the optimization problem studied in this paper is a broader category. The continuous-time algorithm for solving the problem is designed using the Karush-Kuhn-Tucker (KKT) condition in the optimization theory, and when the initial point satisfies certain conditions, the convergence of the algorithm is proved by the principle of set-valued LaSalle invariance. Numerical example illustrates the performance of the proposed algorithm.