This paper presents a communication-less distributed voltage control strategy for a multi-bus AC islanded microgrid. First, a Kalman Filter-based network voltage estimator is proposed to obtain voltage responses without communication links in the presence of load disturbances. Then, a voltage optimal controller using MPC (Model Predictive Control) are developed to implement voltage optimal control. The contributions of this paper are demonstrated: (1) The proposed voltage estimator can dynamically obtain network voltage responses just through local voltage and current associated with each DG (Distributed Generator) unit rather than relying on any communication facilities; (2) In contrast to the conventional PI-based voltage control method, the proposed voltage control strategy can implement not only offset-free control for single-bus, but also optimal control for multi-bus. Thus the flexibility and reliability is improved for islanded microgrids due to communication-less operation. The simulations and experimental results are presented to validate the proposed distributed voltage control strategy.