The paper aimed to devise an alternative algorithm for solving system of linear congruence’s. This algorithm is an extension of the algebraic algorithm which is an alternative method for finding solutions in linear congruence’s. The basic idea of the technique is to convert the given linear congruence’s into linear equations and solve them algebraically. The advantage of this algorithm is the simplicity of its computations and its applicability to systems of linear congruence’s where the conditions of the Chinese Remainder Theorem that the moduli m1…mn should be pairwise cop rime is not satisfied. Some illustrative examples are given to show validity of this method for solving system of linear congruence’s.