Inthispaper,wepresentm-timesecant-likemulti-projectionalgorithmforsparseunconstrainedminimizationproblem.Weprovethismethodareallq-superlinearlyconvergenttothesolutionaboutm≥l.Atlast,wediscussfromsomenumericalresults,howtochoosethenumbermtodeterminetheapproximatingmatrixproperlyinpracticaluse.