Abstract: A new sparse signal recovery algorithm, dubbed as residual minimization pursuit (RMP), is proposed for compressive sensing signal reconstruction. This algorithm iteratively detects the support set of the true signal by selecting the element with the largest magnitude of orthogonal projection of residual signal onto the measurements matrix, and then updates the unknown signal using a least-squares solution on the detecting support set. In addition, two support detection strategies are devised by spotting several elements in each iteration. The experimental studies are presented to demonstrate that the RMP algorithm offers an attractive alternative to OMP for sparse signal recovery.