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With the remarkable increase in the number of nucleotide and acid sequences, it is necessary to study pattern matching in querying sequence patterns in the biological sequence database. To further raise the performance of the pattern matching algorithm, an improved BM algorithm (called BMBR) is presented. It bases on the method of BM algorithm and combines with the shift function of BR algorithm, thus reaches the best shift distance and improves the performance. The best and worst cases in time complexities of the proposed algorithm are also discussed. The experimental results show that the algorithm is faster than other compared algorithms for small alphabets and long patterns, and thus the proposed algorithm is quite suitable for pattern matching in biological sequences.