A double sine basis function neural network for the design of 2D lowpass filters is presented. This neural network is contrived to have an energy function that coincides with the sum-squared error of the approximation problem at hand and by ensuring that the energy is a monotonic decreasing function, the approximation problem can be solved. The training theorem is proposed, and design of the 2D lowpass filters is improved obviously. It conquers the primary disadvantages of the conventional neural networks that the convergence speed is rather low. The simulation results indicate that there are no fluctuation both in the passband and stopband, and it attains near ideal filter attenuation characteristics.