The layer compression modulus B was determined near the smectic-A-smectic-C-alpha* phase transition in an antiferroelectric liquid crystal 4-(1-methylheptyloxycarbonyl)-phenyl 4'-octylbiphenyl-4-carboxylate (MHPBC). The temperature dependence of B clearly defined the smectic-A-smectic-C-alpha* phase transition temperature and supplied a new and clear evidence that the smectic-C-alpha* phase is a tilted phase. The pretransitional softening of B can be represented by a simple power law and explained well by the theoretical description based on renormalization-group method. These results clearly show that the transition is not of the Landau mean-field type.