Time-domain equivalent source method (TDESM) has been employed for indoor simulation of pass-by noise (PBN). Despite removing the requirement of dedicated large semi-anechoic chambers for the microphone array technique, it is still difficult to obtain high simulation accuracy due to the existence of signal splicing error and ill consideration of Doppler effect induced by the vehicle motion. In this article, the TDESM is developed to improve the simulation accuracy of PBN. Unlike the previous TDESM, the improved TDESM (I-TDESM) models the PBN by superposing the contributions of an array of moving equivalent sources, which can take the influence of vehicle motion into account. The PBN at the receivers can be directly reconstructed via the sound field calculation of moving sources. Numerical studies and real vehicle experiments are implemented to demonstrate the feasibility of the I-TDESM. Simulation results show that the I-TDESM can naturally incorporate the Doppler effect and effectively eliminate the signal splicing error, thus improving the simulation accuracy. The experiment results of real vehicle further validate the I-TDESM.