This paper presents an improved virtual synchronous control (VSynC) for the grid-connected voltage source converter (VSC) so as to continuously operate under the grid voltage with steady unbalance. The improved VSynC introduces the negative sequence power controls on basis of conventional VSynC. The improved VSynC is capable of regulating the negative sequence internal voltage to reduce the negative-sequence injected currents and oscillated powers of the VSC aroused by the negative-sequence grid voltage. Three alternative local control objectives for the VSC itself under steady state unbalanced grid conditions and their corresponding power references are deduced and computed. Simulated and experimental results are presented to validate the correctness and effectiveness of the proposed improved VSynC to enhance the continuous operation performance of VSynC-based VSCs during grid voltage steady-state unbalance.