Surface plasmon resonance (SPR) sensor is widely used for its high precision and real-time analysis. Fiber-optic SPR sensor is easy for miniaturization, so it is commonly used in the development of portable detection equipment. It can also be used for remote, real-time, and online detection. In this study, a wavelength modulation fiber-optic SPR sensor is designed, and theoretical analysis of optical propagation in the optical fiber is also done. Compared with existing methods, both the transmission of a skew ray and the influence of the chromatic dispersion are discussed. The resonance wavelength is calculated at two different cases, in which the chromatic dispersion in the fiber core is considered. According to the simulation results, a novel multi-channel fiber-optic SPR sensor is likewise designed to avoid defaults aroused by the complicated computation of the skew ray as well as the chromatic dispersion. Avoiding the impact of skew ray can do much to improve the precision of this kind of sensor.