Spin injection into magnesium from Permalloy is performed in the lateral spin valve geometry. A large spin valve signal of 3.1 mΩ is observed at room temperature. The injector-detector separation dependence of the spin valve signal is analyzed by using a one-dimensional spin-diffusion model. The analysis yields the spin diffusion length of about 200 nm for the Mg nanowires. The short spin diffusion length of magnesium which has a small spin-orbit interaction can possibly be explained by considering the spin-hot-spot relaxation mechanism proposed by Fabian and Das Sarma.