A voltage source converter (VSC) is one of the most widely used power converters in a power system. In this paper, a timedomain-based accelerated steady-state method is proposed to solve for a closed-loop pulse-width modulated (PWM) VSC with dq-frame controllers, which is able to account for the harmonic interactions between the converter and the rest of the power network, between the AC and DC sides of a VSC, and between the converter and its controllers. The proposed time-domain method is based on the modified time-domain shooting method, where the Jacobian matrix is updated by the quasi-Newtons method. This will drastically increase the computation efficiency as it avoids re-evaluating and inverting the Jacobian matrix, whose size is usually very large for a PWM-VSC due to high number of times of switching. All the results are shown to be consistent with those obtained by a PSCAD/EMTDC model, which has been validated with the experiment in a previous publication.