The problem of source coding with side information at the decoder arises in many practical scenarios. Although this problem has been well characterized in information theory, particularly by the work of Wyner and Ziv (1976), there is still lack of successful algorithms for it. In this paper, we use trellis codes to approach the theoretical limit. An embedded trellis code structure is proposed, and its properties are examined. Using this structure, we can achieve the granular gain at the encoder as well as the coding gain at the decoder. Simulation results show that the proposed scheme outperforms the algorithms reported in the literature. It is also indicated that the performance of the proposed algorithm can approach the information-theoretic limit at high rate as the trellis complexity increases.