A virtual power plant (VPP) is aimed to integrate distributed energy resources (DERs). To solve the VPP economic dispatch (VPED) problem, the power supply-demand balance, power transmission constraints, and power output constraints of each DER must be considered. Meanwhile, the impacts of communication time delays, channel noises, and the time-varying topology on the communication networks cannot be ignored. In this paper, a VPED model is established and a distributed primal-dual sub-gradient method (DPDSM) is employed to address the presented VPED model. Compared with the traditional centralized dispatch, the distributed dispatch has the advantages of lower communication costs and stronger system robustness, etc. Simulations are realized in the modified IEEE-34 and IEEE-123 bus test VPP systems and the results indicate that the VPED strategy via DPDSM has the superiority of better convergence, more economic profits, and stronger system stability.