This paper deals with a kind of iterations,which need to solve the symmetric positive definite systems of linear equations whose matrices of coefficients have varying positive semi-definite tri-diagonal martrix increments. The positive semi-definite tri-diagonal martrix increment is especially divided, an iterative algorithm is presented. It to use the algorithm in the iterative process of repeatedly solving above mentioned system. Wu Zhuzhu has presented an algorithm for diagonal elements with positive increments. The algorithm of this paper which takes martrix increments into account, is the generalization of the algorithm presented by Wu Zhuzhu.