In this paper, we propose an approach to improve the sensitivity of an optical fiber surface plasmon resonance (SPR) sensor with a pure higher-order mode excited by a designed mode selective coupler (MSC). We calculate the proportion of the power of the higher-order mode in the cladding. Compared to the LP01 mode, the power proportion of the LP11 mode (LP21 mode) in the cladding theoretically improves by 100% (150%). To generate a relatively pure LP11 mode or LP21 mode, a mode selective coupler (MSC, 430–580 nm) is designed. The coupling efficiency of the LP01–LP11 mode coupler is over 80%, and that of the LP01–LP21 mode coupler is over 50%. The simulation results show that the sensitivity of the LP11  mode and the LP21 mode increases by approximately 330% and 360%, respectively, using the intensity modulation (n = 1.33–1.38, 430–580 nm); the resolution of the refractive indices of our sensor, using the LP11 mode (LP21 mode), is 2.6×10−4 RIU (2.4×10−4 RIU). The higher sensitivity and resolution of our presented fiber SPR sensor containing a visible MSC make it a promising candidate for the measurement of refractive indices.