The compounds RNi2Mn (R=Tb,Dy,Ho,andEr) with a MgCu2-type structure have been synthesized. The R to transition metal atom ratio is confirmed to be 1:3 using the energy dispersive spectroscopy. The structural and magnetic properties have been investigated by various experimental methods. The x-ray diffraction patterns (XRD) can be well indexed with a cubic Laves cell and space group Fd3m. The refinement results of the XRD patterns show the presence of vacancies in the crystallographic structure. The ordering temperatures TC have been derived to be 131, 94, 75, and 50K for R=Tb,Dy,HoandEr, respectively, which are much higher than those of their corresponding RNi2 and RMn2 compounds. A large difference of M-T curves between zero-field-cooling and field-cooling magnetization for all samples at a certain temperature range is observed in a low field, which can be understood in the terms of narrow-domain-wall pinning and a sensitive temperature dependence of coercivity.