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In this paper, in order to achieve low differential mode group delay (DMGD) over the C±L band, we propose the hole-assisted graded-index few mode fiber (FMF) design supporting four nondegenerated linear polarized (LP) modes for a mode division multiplexing system. In order to determine the fiber core parameters, an optimization has been made between the enlargement of the effective area (Aeff) and the reduction of macrobending loss (MBL). The A_eff about 107 μm² for LP₀₁ mode at the wavelength of 1550 nm and the MBL lower than 0.005 dB/100 turns for LP₀₂ mode at the curvature radius of 30 mm and at the wavelength of 1550 nm are achieved simultaneously. The numerical simulation results prove that the hole-assisted structure can greatly reduce the absolute value of DMGD of the FMF. Particularly, the maximum DMGD less than |35| ps/km within the spectrum range from 1530 to 1630 nm is achieved. A tolerance analysis against manufacturing errors has been discussed, and we further propose a self-managed low DMGD transmission line solution with the controllable air-hole size.