The traditional convolution algorithm in discrete wavelet transform (DWT) usually makes use of extension to conquer the boundary effect, thus the processing speed is influenced. To further improve the real-time performance of DWT, a novel fast algorithm for implementing discrete convolution is proposed. This approach uses the convolution result at two ends to correct the boundary wavelet coefficients, so the boundary effect of convolution operation is effectively solved and the computational complexity is reduced. Simulation experiment and engineering application results show that the proposed algorithm is suitable for analyzing stationary signals and nonstationary signals, and it has high decomposition/reconstruction accuracy and good boundary processing performance. Moreover, its calculation speed is much faster than that of the traditional method. Hence it has remarkable engineering value.