In this paper, the authors present the influence of annealing conditions on structure an4 magnetic behavior of Ni50Mn37Sn13 magnetocaloric alloy prepared by arc-melting technique. The results show that the almost single phase of the full Heusler structure of Ni2MnSn could be achieved by appropriate annealing. The transformation between martensite and austenite phases, and multi-magnetic phase behavior are observed more clearly with higher fraction of Ni2MnSn phase. By using Arrott-Noaks method, critical parameters were determined to be Beta = 0.464 + or - 0.021, Gama = 1.117 + or - 0.073 and Delta = 3.41, which lay between mean-field model Beta = 0.5 and Gama = 1,Delta = 3) with long-range ferromagnetic orders and 3D Heisenberg model (Beta = 0.365, Gama = 1.336, Delta = 4.66) with short-range ferromagnetic orders. The calculated results are in good accordance with the experimentally observed coexistence of weak-ferromagnetic martensite and strong1erromagnetic austenite phases.