As compared to the well-known traditional couple-mode theory, in this study, we proposed a visual, graphical, and simple numerical simulation method for long-period fiber-grating surface-plasmon-resonance (LPG-SPR) sensors. This method combines the finite element method and the eigenmode expansion method. The finite element method was used to solve for the guided modes in fiber structures, including the surface plasmon wave. The eigenmode expansion method was used to calculate the power transfer phenomenon of the guided modes in the fiber structure. This study provides a detailed explanation of the key reasons why the periodic structure of long-period fiber-grating (LPG) can achieve significantly superior results for our method compared to those obtained using other numerical methods, such as the finite-difference time-domain and beam propagation methods. All existing numerical simulation methods focus on large-sized periodic components; only the method established in this study has 3D design and analysis capabilities. In addition, unlike the offset phenomenon of the design wavelength λ(D) and the maximum transmission wavelength λ(max) of the traditional coupled-mode theory, the method established in this study has rapid scanning LPG period capabilities. Therefore, during the initial component design process, only the operating wavelength must be set to ensure that the maximum transmission wavelength of the final product is accurate to the original setup, for example, λ = 1550 nm. We verified that the LPG-SPR sensor designed in this study provides a resolution of ~-45 dB and a sensitivity of ~27000 nm/RIU (refractive index unit). The objective of this study was to use the combination of these two numerical simulation methods in conjunction with a rigorous, simple, and complete design process to provide a graphical and simplistic simulation technique that reduces the learning time and professional threshold required for research and applications of LPG-SPR sensors.