The dendritic growth in an undercooled melt of pure substance is simulated by a phase_field model. The relationship between the dendritic growth and the parameters used in phase_field method (including undercooling, anisotropic coefficient, magnitude of thermal fluctuation) has been studied quantitatively. By employing the thermal fluctuations the birth of secondary branches has been successfully simulated. The spacing and amplitude of the secondary branches are obtained, which are in reasonable agreement with those by using the Wentzel_Kramers_Brillouin approach. Simulations indicate that the undercooling and the anisotropic coefficient have remarkable influence on the growth of the secondary branches, in which secondary branch spacing decreases with the increase of undercooling, but increases with the increase of anisotropic coefficient. The amplitude of the secondary branch decreases with the increase of anisotropic coefficient. Thermal fluctuations show strong influence on the amplitude of the secondary branch, however show less influence on the secondary branch spacing.