In this paper, we present a symbol-level joint source-channel decoding (JSCD) algorithm for transmission of convolutionally encoded variable-length codes (VLCs). The proposed algorithm is based on a two-dimensional state representation which leads to a three-dimensional code trellis. JSCD on this trellis is realized by employing a modified BCJR algorithm which allows to fully exploit the symbol-level source a priori information. Experimental results indicate that the proposed JSCD scheme achieves high robustness against channel noises.