Lakovic et al. presented an algorithm for jointly decoding a Huffman and convolutionally encoded data sequence with significant improvement in error rates relative to a traditional system in which source and channel decoding are performed separately. However, it has a serious drawback that, for long source sequence, the decoding complexity becomes quite expensive due to the enormous number of trellis states. In this work, a new path metric with low computational complexity is derived first, and then based on a code trellis rather than on a code tree, we proposed a joint Huffman and convolutional soft-decision priority-first decoding algorithm. Simulation results indicate that the proposed decoding algorithm provides nearly the same performance as that in Lakovic's scheme while exhibiting a significantly lower complexity.