The optimized crystal structure, energy band, density of states, and optical properties of 0.5NdAlO3-0.5CaTiO3 are calculated by the plane wave ultrasoft pseudopotential method based on the first-principles density functional theory. The optimized crystal parameters are in good agreement with the experimental ones and the errors are less than 1%. The calculated energy band results indicate that 0.5NdAlO3-0.5CaTiO3 has an indirect band gap of 0.52 eV. The energy band near Fermi level is determined by the density of states of Nd-4f, O-2p, Nd-4p, Al-3p, Ti-4d electrons. Moreover, the dielectric function, reflectivity and refractive index of 0.5NdAlO3-0.5CaTiO3 are also calculated.