A series of Ni45Mn44-xCrxSn11 (x = 0, 1, 2) ferromagnetic shape memory alloys were prepared. With slight doping of Cr, the martensitic transition temperatures decrease rapidly. The magnetic entropy changes at a low magnetic field were investigated in these alloys. The maximum value of ∆SM is 23.4 J kg-1 K-1, which was observed in Ni45Mn43CrSn11 alloys. The origin of the magnetic entropy changes in these alloys has been discussed. The giant low-field magnetic entropy changes and low cost make Ni45Mn44-xCrxSn11 alloys a promising candidate for magnetic refrigeration.