The generator polynomial estimation of a pseudo-random sequence in truncated codes or error codes is studied in the paper. An optimum estimation algorithm for the generator polynomial via a match-searching is proposed by constructing verification equations based on the linear principle of the pseudo-random sequence. The important characteristic of reducible polynomial in GF(2) is used by reducing the computational amount in algorithm optimization. Finally, the estimation performance of the algorithm at different thresholds and bit errors is simulated,and the performance of the algorithm for the truncated codes or error codes is compared with that of the typical algorithm by taking m-sequences as an example. Simulation results indicate that the algorithm has good adaptability for the error codes and truncated codes and it completes a estimation for the m-sequences with rank of 15 and can adapte to an error rate more than 20%. The algorithm can preferably meets engineering application requirements.