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We measured the low-temperature specific heat in magnetic fields up to 80 kOe, together with the magnetization for the heavy-fermion superconductor CeCoIn5 with the transition temperature Tc ¼ 2: 25 K. CeCoIn5 is a strong-coupling superconductor with a large jump in the specific heat ÁC= CnðTcÞ ¼ 4: 7. The heavy-fermion state is significantly formed below 1 K, reaching at least 1070 mJ/K2Ámol in magnetic fields. This large electronic specific heat coefficient at 0.25 K is, however, reduced with increasing magnetic field, ranging from 1070 mJ/K2Ámol at 50 kOe to 820 mJ/K2Ámol at 80 kOe. The upper critical field Hc2 at 0 K is estimated to be 116 kOe for H k ½100 and 49.5 kOe for H k ½001. The present anisotropy of Hc2 is well explained by the anisotropic effective mass, but the magnitude of Hc2 is reduced strongly by the paramagnetic effect for both field directions.