Abstract: In this paper the theory and method of time-domain inversion for the asymmetric seismic moment tensor are studied based on the symmetric seismic moment tensor inversion. It is shown that the asymmetric seismic moment tensor inversion is analogous to the symmetric one, and that only a minor modification on the method of symmetric seismic moment tensor inversion, i.e., increasing three unknown parameters is required to realize the asymmetric seismic moment tensor inversion. The Akaike Information Criterion (AIC) is introduced to judge whether the asymmetric seismic moment tensor inversion is over fitting as compared with the symmetric seismic moment tensor inversion. In analyzing the asymmetric seismic moment tensor the vector representation of the moment tensor is introduced to describe the difference between seismic moment tensors quantitatively. By analyzing the relation between Green's function and each of moment tensor's components, it is found that, in asymmetric seismic moment tensor inversion, the components M_xy and M_yx could not be distinguished if only vertical displacement data were used in inversion. The vertical and horizontal displacement data should be used jointly in inversion to distinguish M_xy from M_yx. It is also found that if a different velocity structure model or a different method for calculating the Green's function was adopted for the inversion, the resolutions between any seismic moment tensor components need to be re-analyzed. A series of numerical tests were performed to test the feasibility of the present inversion method by using synthetic data. It is shown that the present inversion method is feasible and that it is necessary to use jointly both the P and S wave data to invert for the asymmetric seismic moment tensor.