This paper proposes a bi-directional associative neural network for the singular value descomposition (SVD) of a non-squares matrix. The task of finding the SVD of a non-squares matrix is achieved by finding the limiting solution of the differential equation governing this network. By Lasalle' invariance principle and Liapunov's indirect method, we strictly investigate its global asymptotical stability. Its performance is evaluated by way of analysis and computer simulations. In simulations, in order to quicken the converging speed and the stability of the iteration algorithms uniformly, let learning rates be time-varying or adaptive. The simulation results show that this neural network is exponentially convergent near the stable equilibrium poits. This neural network maintains the bi-directional associate structure in the classical SVD. The method is inspired by the power of parallel processing and ability of a differencial equation approach to deal with time-varying or adaptive tasks.