Based on the time dependent theory, the random laser emission in two-dimensional disordered medium with different pumping rates and refractive indices is calculated. The spatial distributions of emission spectra and lasing modes are also analyzed. The calculated results show that the larger the difference of refractive index between scattering medium and background medium is, the smaller the lasing threshold is. The emission spectra of different regions are different, and change with the intensity of pump source. The lasing emission is mainly distributed in some certain regions, the pumping efficiency is different for these certain regions, and spatial extent overlap of modes is produced between regions.