In the field of signal processing, many problems can be formulated as optimization problems. And most of these optimization problem can be further described in a formal form, that is binary quadratic programming problem(BQP). However, solving the BQP is proved to be NP-hard. Due to this reason, many novel algorithms have been proposed in order to improve the efficiency to solve the BQP [4]. In this paper, polynomial algorithms to binary quadratic programming problems with Q being a tri-diagonal or five-diagonal matrix is focused by taking advantage of the basic algorithm proposed in [1], [17], [3]. The basic algorithm is firstly reviewed and then this algorithm is modified to solve binary quadratic programming problems with Q being a tri-diagonal. Furthermore, by improving this algorithm, an algorithm is proposed to solve binary quadratic programming problems with Q being a five-diagonal matrix.