Temperature dependence of the spin-lattice relaxation time T-1 was measured in an antiferroelectric liquid crystal, 4-(1-methylheptyloxycarbonyl) phenyl-4'-octyloxybiphenyl-4-carboxylate (MHPOBC) by means of C-13-nuclear magnetic resonance (NMR). The activation energies determined by the temperature dependence of T-1 are the same for most of the carbon nuclei in the SmA and SmCA* phases, whereas they are different for carbon nuclei at the chiral center and at the carbonyl carbons. The rotational correlation time changes continuously through the phase change from SmA to SmCA*. Critical slowing down of the molecular rotatioin was not observed.