A new and efficient numerical method to solve acoustic scattering in the time domain is presented in the present paper. Equivalent sources are embedded within a scattering surface and their strengths are determined as a function of time by the pressure-gradient boundary condition on a scattering surface. Once the strengths are determined, the equivalent sources are used to predict the scattered pressure. Linear shape functions are used to discretize the strength of the equivalent sources in time and singular value decomposition is used to find the least-squares solution and to overcome potential numerical instabilities. The predictions are found to be in excellent agreement with the exact solutions for sound from a point monopole source and band-passed broadband sound. The method works well even at the irregular frequencies at which internal resonance modes occur. Finally, the method is used to predict the scattering of sound from a moving source. It is shown that the method has the capability to capture aperiodic characteristics very well.