Abstract: An algorithm is presented for solving quasi quinque-diagonal linear system of equation. First, the last two variables are selected as the parameters and are put into the other n-2 equations. Then the original problem can be transformed into a problem for solving three quinque-diagonal linear systems of equation. Finally, all the solution vectors can be obtained by solving the parameters xn-1 and xn. A forward elimination and backward substitution algorithm is used to solve the quasi quinque-diagonal linear system, it shows a good numerical stability. Experimental data indicate that comparing with the four parameter algorithm, not only the two parameter method is fast for solving the same order of linear equations with time ratio of about 1.47, but also the memory consumption is less than that used by the four parameters. The measure of multiplication or division in this algorithm is O(23n) and O(16n) for addition and subtraction, respectively. The memory needed is about O(10n). The number of arithmetical operations and memory consumption all have a linear relation with the n.