We propose a kind of trench-assisted graded-index ring-core fiber (TA-GI-RCF) with a low refractive index rod deployed in the center of the core, which supports three LP modes (LP01, LP11 and LP21) transmission. There are two difficulties about designing TA-GI-RCF, one is to depart LP21 mode from LP02 mode because their effective indices are too close which makes it difficult to realize only three LP modes transmission; the other one is how to make sure these three LP modes reach the receiver end with low differential mode delay (DMD), so that the computation complexity of multi-input multi-output (MIMO) digital signal process (DSP) can be reduced. At first, we realize the separation of LP21 mode and LP02 mode in TA-GI-RCF by enlarging the size of low refractive index rod. We next investigate the influence of the TA-GI-RCF structural parameters on DMD and DMD slope, and find that a graded-index core and a low refractive index rod can flexibly tune the DMD, and a trench can flexibly control the DMD slope. Through optimizing the core parameters, we find that the design region of α is 1.01~2.23 and that of Δ1 is 0.28%~0.46% at r1=30 μm, where α is the profile exponent and Δ1 is the relative refractive index difference between core and cladding. Simulation results show that TA-GI-RCF can achieve the effective area (Aeff) of LP01 mode over 2000 μm2 and the |DMD| between LP01 mode and LP11 mode is ≤100 ps/km over C+L band. Above all, we can achieve three LP modes transmission in TA-GIRCF with low DMD over whole C+L band and large Aeff.