Reversibility　of　the　magnetocaloric　effect　in　materials　with　first-order　magnetostructural　transformation　is　of　vital　significance　for　practical　magnetic　refrigeration　applications.　Here,　we　report　a　large　reversible　magnetocaloric　effect　in　a　Ni49.8Co1.2Mn33.5In15.5　magnetic　shape　memory　alloy.　A　large　reversible　magnetic　entropy　change　of　14.6　J/(kg　K)　and　a　broad　operating　temperature　window　of　18K　under　5　T　were　simultaneously　achieved,　correlated　with　the　low　thermal　hysteresis　(similar　to　8K)　and　large　magnetic-field-induced　shift　of　transformation　temperatures　(4.9K/T)　that　lead　to　a　narrow　magnetic　hysteresis　(1.1　T)　and　small　average　magnetic　hysteresis　loss　(48.4　J/　kg　under　5　T)　as　well.　Furthermore,　a　large　reversible　effective　refrigeration　capacity　(76.6　J/　kg　under　5　T)　was　obtained,　as　a　result　of　the　large　reversible　magnetic　entropy　change,　broad　operating　temperature　window,　and　small　magnetic　hysteresis　loss.　The　large　reversible　magnetic　entropy　change　and　large　reversible　effective　refrigeration　capacity　are　important　for　improving　the　magnetocaloric　performance,　and　the　small　magnetic　hysteresis　loss　is　beneficial　to　reducing　energy　dissipation　during　magnetic　field　cycle　in　potential　applications.　(C)　2016　AIP　Publishing　LLC.