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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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>LP</mi></mrow><mrow><mn>01</mn></mrow></msub></mrow></semantics></math></inline-formula> mode, the power proportion of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>LP</mi></mrow><mrow><mn>11</mn></mrow></msub></mrow></semantics></math></inline-formula> mode (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>LP</mi></mrow><mrow><mn>21</mn></mrow></msub></mrow></semantics></math></inline-formula> mode) in the cladding theoretically improves by 100% (150%). To generate a relatively pure <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>LP</mi></mrow><mrow><mn>11</mn></mrow></msub></mrow></semantics></math></inline-formula> mode or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>LP</mi></mrow><mrow><mn>21</mn></mrow></msub></mrow></semantics></math></inline-formula> mode, a mode selective coupler (MSC, 430–580 nm) is designed. The coupling efficiency of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>LP</mi></mrow><mrow><mn>01</mn></mrow></msub><mo>–</mo><msub><mrow><mi>LP</mi></mrow><mrow><mn>11</mn></mrow></msub></mrow></semantics></math></inline-formula> mode coupler is over 80%, and that of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>LP</mi></mrow><mrow><mn>01</mn></mrow></msub><mo>–</mo><msub><mrow><mi>LP</mi></mrow><mrow><mn>21</mn></mrow></msub></mrow></semantics></math></inline-formula> mode coupler is over 50%. The simulation results show that the sensitivity of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>LP</mi></mrow><mrow><mn>11</mn></mrow></msub><mo> </mo></mrow></semantics></math></inline-formula> mode and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>LP</mi></mrow><mrow><mn>21</mn></mrow></msub></mrow></semantics></math></inline-formula> mode increases by approximately 330% and 360%, respectively, using the intensity modulation (<i>n</i> = 1.33–1.38, 430–580 nm); the resolution of the refractive indices of our sensor, using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>LP</mi></mrow><mrow><mn>11</mn></mrow></msub></mrow></semantics></math></inline-formula> mode (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>LP</mi></mrow><mrow><mn>21</mn></mrow></msub></mrow></semantics></math></inline-formula> mode), is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.6</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></semantics></math></inline-formula> RIU (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.4</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></semantics></math></inline-formula> 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.