A novel type of few-mode fiber, characterized by an inverse-parabolic graded-index profile, is proposed for the robust transmission of cylindrical vector modes as well as modes carrying quantized orbital angular momentum (OAM). Large effective index separations between vector modes (>2.1 × 10(-4)) are numerically calculated and experimentally confirmed in this fiber over the whole C-band, enabling transmission of OAM(+/-1,1) modes for distances up to 1.1 km. Simple design rules are provided for the optimization of the fiber parameters.