The Fast Wavelet Collocation Method (FWCM) is a recently proposed circuit simulation approach, which is very promising in achieving uniform error distribution and handling singularities in high-speed circuits, compared with conventional time domain simulation methods. In this paper, we aim to extend the wavelet collocation method to the simulation of large-scale circuits, where a large dimension Sylvester equation needs to be solved. The performance of the wavelet simulator is dominated by the time and memory consumption of the Sylvester equation solver. In order to improve the simulation efficiency, we propose a direct method to solve the Sylvester equation by Schur decomposition. Numerical experiments demonstrate that the proposed simulator can achieve higher computation speed and higher simulation accuracy as well as more robust convergence than SPICE.