We have synthesized polycrystalline and single-crystalline samples of SmPtSi2, and measured their resistivity, specific heat, magnetization, and Seebeck coefficient. The existence of two magnetic phase transitions has been confirmed, one at T
H = 8.6 K and the other T
L = 5.6 K. A hump-type anomaly in resistivity, a lambda-type anomaly in specific heat, a downward bend in magnetization, and a semiconductor-like increase in the Seebeck coefficient were observed at T
H, indicating an antiferromagnetic transition accompanied by a gap opening on the Fermi surface. In contrast, a sharp drop in resistivity, a sharp spike in specific heat, and a drop in magnetization were observed at T
L. The Seebeck coefficient showed metallic temperature dependence below T
L. With increasing pressure, T
H and T
L shifted to higher temperatures. The transition at T
L was no longer observed at pressures above 1.5 GPa. These findings suggest that the transition at T
L is a transition from an antiferromagnetic ordered state with the gap on the Fermi surface to a different antiferromagnetic state.