In this note we propose an algorithm based on the Lanczos bidiagonalization to approximate the backward perturbation bound for the large sparse linear squares problem. The algorithm requires $$\mathcal{O}$$ ((m + n)l) operations where m and n are the size of the matrix under consideration and l <#60;<#60; min(m,n). The import of the proposed algorithm is illustrated by some examples coming from the Harwell-Boeing collection of test matrices.