In this paper, a distributed synergetic control based on multi-agent systems is proposed to solve the problems of frequency and voltage errors, system stability and power sharing accuracy in the traditional droop control of microgrids. Starting with power flow equations, we build the secondary-order dynamic model of DG, which consists of three parts: (1) active power allocation; (2) active power-frequency; and (3) reactive power-voltage droop control. Considering time-delays in communication networks, a leaderless synergetic control algorithm is proposed to allocate the active power in inverse proportion to the droop coefficient, and the synergetic control with a virtual leader is proposed to control the system frequency and voltage to keep at the expected value. Besides, the direct Lyapunov method is introduced to verify the globally asymptotical stability. Moreover, the impacts of communication disturbance are also discussed from the aspects of control precision and system stability. Finally, based on a test microgrid, numerous cases are designed as illustration, and the simulation results validate the proposed method.