We have theoretically analyzed the influence of skew rays on the performance of a fiber-optic sensor based on surface plasmon resonance. The performance of the sensor has been evaluated in terms of its sensitivity and signal-to-noise ratio (SNR). The theoretical model for skewness dependence includes the material dispersion in fiber cores and metal layers, simultaneous excitation of skew rays, and meridional rays in the fiber core along with all guided rays launching from a collimated light source. The effect of skew rays on the SNR and the sensitivity of the sensor with two different metals has been compared. The same comparison is carried out for the different values of design parameters such as numerical aperture, fiber core diameter, and the length of the surface-plasmon-resonance (SPR) active sensing region. This detailed analysis for the effect of skewness on the SNR and the sensitivity of the sensor leads us to achieve the best possible performance from a fiber-optic SPR sensor against the skewness in the optical fiber.