The moving vehicle loads on a bridge deck is one of the most important live loads of bridges. They should be understood, monitored and controlled before the bridge design as well as when the bridge is open for traffic. A MOM-based algorithm (MOMA) is proposed for identifying the timevarying moving vehicle loads from the responses of bridge deck in this paper. It aims at an acceptable solution to the ill-conditioning problem that often exists in the inverse problem of moving force identification. The moving vehicle loads are described as a combination of whole basis functions, such as orthogonal Legendre polynomials or Fourier series, and further estimated by solving the new system equations developed with the basis functions. A number of responses have been combined, some numerical simulations on single axle, two axle and multiple-axle loads, being either constant or timevarying, have been carried out and compared with the existing time domain method (TDM) in this paper. The illustrated results show that the MOMA has higher identification accuracy and robust noise immunity as well as producing an acceptable solution to ill-conditioning cases to some extent when it is used to identify the moving force from bridge responses.