Herein, we report on the experimental observations and a quantitative determination of the laser-induced frequency shift (LIFS) in the photoassociation (PA) spectra of spinor Bose-Einstein condensate of sodium. Our investigations revealed a nonlinear dependence of the LIFS on the intensity of PA laser. By developing a model within the quadratic Stark effect, we simulate the experimental results via a theoretical model that confirms the former. The experimental observations and the theoretical analysis can further improve the accuracy of investigations on important molecular properties and on preparation of specific molecular states, with possible applications in various key fields.