This paper proposes a novel refractive index profile design based on few-mode fibers (FMFs) which can support 4 linear polarization (LP) modes. We first present a FMF whose core is dually assisted by a nano-hole (NH) and a high-index-ring (HIR), and then substitute the dual assistance by an innovative graded concave HIR (GC-HIR) assisted structure. Using the finite element method (FEM), the parameters of the NH-HIR and GC-HIR optical fiber are adjusted to investigate their respective minimum effective refractive index difference (minΔn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> ), which is 2.012 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> for the former, and 2.532 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> for the latter. Both optical fibers have a significant improvement on the crosstalk suppression effect, and the GC-HIR optical fiber is even better. The proposed GC-HIR FMF with special refractive index profile has potential application prospects in mode division multiplexing (MDM) optical fiber communication system, and can provide theoretical foundation for the design and analysis of subsequent optical fibers and key components.