This paper investigates a distributed convex optimization with local constraint sets over weight-balanced directed networks,where the global objective function is described as a sum of some agents' local objective functions.To solve this problem in a distributed way,the problem is transformed into a Fenchel dual problem by introducing local conjugate functions.Then,for the Fenchel dual problem,a distributed continuous-time algorithm is proposed based on the singular perturbation system.When the local objective functions are strongly convex and their gradients are Lipschitz continuous,it is shown that the primal and dual optimality can be both achieved by using the tools from convex analysis and Lyapunov stability.Finally,simulation results are given to illustrate the effectiveness of the proposed algorithm.