The ac susceptibility of single crystals of Nia single-molecule magnets is measured by a compensation measurement setup. The magnetic relaxation time calculated from the peak of the out-phase component of the susceptibility fits the Arrhenius law well and gives an effective spin-flipping energy barrier of Ueff = 7.2 K. This value is far below the classical activation energy barrier of U = 14 K, whereas it is close to the energy gap between the Sz = ±4 and Sz = ±3 doublets, which indicates that quantum tunneling between the Sz ＝ 3 and Sz = -3 states plays a key role in the magnetic relaxation. Therefore the relaxation process combines thermal activation and quantum tunneling. Also we deduce that the blocking temperature of Ni4 single-molecule magnets is lower than 0.3 K by extrapolating the relaxation time plot, which ensures that this single-molecule magnet material enters a long-range magnetic ordered state instead of a spin glass state at 0.91 K.