Symmetric filters and symmetric extension of image edges have been widely used in wavelet image compression. Since the filters are symmetric, it is possible to take advantage of the symmetric property to reduce the computational complexity for the filtering. In this paper, we present a fast convolution algorithm for the discrete wavelet transform (DWT) and the inverse DWT (IDWT) such that the transform time can be greatly reduced. Compared with regular convolution, the new algorithm can decrease the multiplication operations by nearly one half. Converted into real programming, it sped up the DWT and IDWT in our experiments by at least 12% and 55%, respectively. Incorporated with enhancing zerotree coding, the proposed algorithm results in a rapid and efficient coder. Experimental results showed that the coder is competitive with other high performance coders. The proposed convolution algorithm is also suitable for many types of wavelet‐based coding, including wavelet video coding.