In　the　compressive　sensing　reconstruction　algorithm,　the　unknown　sparsity　and　the　fixed　step-size　are　the　factors　that　affect　the　reconstruction　accuracy　and　running　time　of　the　algorithm.　In　view　of　the　above　shortcomings,　we　propose　a　regularized　backtracking　adaptive　pursuit　algorithm　based　variable　step-size.　Firstly,　the　sparsity　of　the　signal　is　obtained　by　the　way　of　atomic　matching　test.　Then　we　combine　the　regularization　method　with　the　subspace　tracking　algorithm　to　achieve　the　second　screening　and　remove　the　atoms　which　are　not　appropriate.　Finally,　we　use　a　variable　step-size　to　select　atoms　in　the　candidate　set　so　that　we　can　complete　the　signal　reconstruction.　The　simulation　results　show　that　the　proposed　algorithm　is　superior　to　other　algorithms　in　speed　and　reconstruction　accuracy.　©　2018,　Chinese　Institute　of　Electronics.　All　right　reserved.