Mars has two satellites, Phobos and Deimos. The Martian satellites have never been explored from the aspect of elemental composition. Their origins are still mysterious. Gamma-ray spectroscopy from the orbit of spacecraft is a powerful method to investigate elemental distribution and abundance of planets with no or thin atmosphere. In this work, gamma-ray emission from the Martian satellites was calculated as a function of elemental composition. Both chondritic and Martian compositions, which represent captured origin and giant impact origin, respectively, were assumed as elemental composition of Martian satellites. The gamma-ray fluxes induced by galactic cosmic rays at their surface were calculated for both of them. It was found that the elemental compositions of Martian satellites are clearly distinguished between chondritic or Martian by the gamma-ray emission rate ratios of Si/Fe and Ca/Fe and enable us to give strong constraint to the idea for the origin of the Martian satellites.