LaOs 4 P 12 is known as a superconductor with a T c of 2.0 K. The low-temperature specific-heat and the electrical resistivity measurements under magnetic fields using high quality samples revealed that LaOs 4 P 12 is not a simple superconductor. Another phase transition with a transition temperature which is very close to T c exists. The electrical resistivity shows an increase below 3.5 K. The newly found transition disappears by small amount of Ce-impurity.