We consider nonlinear pulse propagation through a fiber Bragg grating with Kerr nonlinearity and linear coupling effects. Using the Stokes parameters, we obtain a set of four equations from the nonlinear coupled-mode equations. From these equations we find the relation for energy density of a gap soliton and construct a quartic anharmonic oscillator equation after finding the appropriate conserved quantities. With the help of the anharmonic oscillator equation we investigate the bright gap soliton solution and as a special case we also obtain another bright gap soliton solution that resembles the solutions of two coupled nonlinear equations for the envelopes of the fundamental and the second-harmonic field components. Moreover, we analyze the motion of the photon in two different potential wells. Finally, we carry out a linear stability analysis to study the stability of the system. © 2003 Optical Society of America.