In this paper, an algorithm for computing the sparse approximate inverse factor of matrix $A^{T};A$, where A is an $m;{ imes};n$ matrix with $m;{geq};n$ and rank(A) = n, is proposed. The computation of the inverse factor are done without computing the matrix $A^{T};A$. The computed sparse approximate inverse factor is applied as a preconditioner for solving normal equations in conjunction with the CGNR algorithm. Some numerical experiments on test matrices are presented to show the efficiency of the method. A comparison with some available methods is also included.