The low temperature specific heat of R 5 Rh 6 Sn 18 (R = Y, Lu) was measured under various magnetic fields (H) up to 8 T. In a zero field, electronic specific heat of Y 5 Rh 6 Sn 18 shows a T 3 dependence, indicating an anisotropic superconducting gap, although that of Lu 5 Rh 6 Sn 18 shows an exponential dependence. In addition, the coefficient of the T -linear term γ(H) of Y 5 Rh 6 Sn 18 in specific heat in the mixed state is found to obey a square root dependence. This is another evidence that Y 5 Rh 6 Sn 18 has the anisotropic superconducting gap. On the other hand, the γ(H) of Lu 5 Rh 6 Sn 18 shows linear dependence, which means the isotropic superconducting gap.