For multi-variable linear/nonlinear regression systems, this paper combines the coupling identification idea with the finite-data-window with forgetting factors theory to present a coupled finite data-window RLS algorithm with forgetting factors. Because the proposed algorithm can avoid the matrix inversion at each recursive calculation and can overcome the data saturation phenomenon, it not only has a highly efficient computation, but also tracks effectively the time-varying parameter and obtains accurate parameter estimates. The application example of parameter identification of the permanent magnet synchronous machine based on the multi-variable model shows the effectiveness and feasibility of the proposed algorithm.