Surface reaction on interstellar ice grains is a key process for the chemical evolution in molecular clouds. We have performed a series of experiments to simulate the chemical evolution of the primordial CO molecule on the ice grains. Photochemical and hydrogen atom reactions of CO-H2O binary ice at 15 K were studied because those are anticipated to be the most dominant chemical processes on the surface of grains. It was found that the photochemical reactions produce CO2 with the highest yield, HCOOH, H2CO, CH3OH, and so on and that even at very low temperatures (much lower than activation energies), addition reactions of hydrogen atoms to CO proceed efficiently due to the tunneling effect and produce H2CO and CH3OH. Branching ratio of the yields in photochemical reactions strongly depends on the structure of ice, while hydrogen atom reactions are very sensitive to both the structure and temperature of ice. Considering the physical and chemical conditions of molecular clouds, the experimental results are consistent with the astronomical observation of ice grains.