Polarization properties of gratings become a research hotspot of fiber Bragg grating based sensors. A new pressure measurement method based on the first normalized Stokes parameter s1 is analyzed. The relationship between s1 parameter and linear birefringence is studied and the causal model of s1 parameter, linear birefringence and pressure is given. The effects on s1 parameter of incident angles of linearly polarized light are researched. The results show that the base value and linearity of s1 parameter are affected by the incident angles of linearly polarized light. A real-time pressure measurement system with fiber Bragg gratings and in-line polarimeter is set up. The curves of s1 parameter with different pressure values are measured and the feasibility of the theory is proved.