Inelastic neutron-scattering measurements have been carried out to study the spin dynamics of La_1-xCa_xMnO₃ single crystals with x=0.05, 0.15, and 0.20. We observed a spin gap of 1.2 meV at the zone center along the [110]^* direction with x=0.05, whereas the gaps of 1.0 meV and 0.9 meV are observed at the zone boundary along the [101]^* direction with x=0.15 and 0.20, respectively. Magnetization measurements on powder samples under the magnetic field of 0.5 T show the reduction of ferromagnetic saturation moment M_sat (5 K) with increasing x. We observed, for x=0.15, a clear difference in M-T curves obtained after field cooling and zero-field cooling under the magnetic field of 0.01 T, indicating a cluster-glass-like nature.