Experimental measurement and analysis of the laser-induced frequency shifts (LIFSs) of photoassociation (PA) spectra in a spinor Bose-Einstein condensate (BEC) of sodium is reported. The trap loss spectra of the atoms in the BEC were recorded at different PA laser intensities. Linear variations of the frequency shift for different spin components were demonstrated. The analogous linear dependence on the intensity of the full width at half maximum (FWHM) of the spectra was also shown. The slopes of the linear relationships of the shift and broadening are both independent of spin component within the error range of the experiment. A theoretical model, considering the interactions of three channels (a scattering continuum state, a single bound level near the scattering state, and an optically excited light-dressed level), explains the linear dependence of the LIFSs and the FWHM broadening on the PA laser power. The experimental results are consistent with the theoretical calculations.