Within the framework of coevolution between the central black hole and the host spheriod galaxy, the black hole growth has been investigated, the associated luminosity function of active galactic nuclei at different redshift has been calculated. Compared with the results of all kinds of deep survey observations, the semi-analytic results provide the fully explanation for the downsizing features. On the other hand, star formation processes, dust absorption and ohther stellar population properties in the primeval galaxies at high redshift, make the tight constraints on the research of cosmic reionization.