The characteristics of dual-color emission and mode competition in two-dimensional random medium are studied. Based on the time-dependent theory, a model for dual-wavelength random laser is established. The Maxwell equations and rate equations are combined and solved by using the finite different time domain (FDTD) method. Light emission spectrum is calculated by Fourier transform. The effects of dye concentration, surface filling-fraction and scatterer radius on random laser emission are discussed. Results show that the emission intensity of long wavelength increases while that of short wavelength decreases with the dye concentration raising . The surface filling-fraction increase the emission intensity and has the same effect on different wavelengths, while the effect of the scatterer radius on the emission spectrum is wavelength dependent.