An anti-parabolic erbium-doped fiber is proposed to effectively separate the degenerate vector modes in the second-order mode group. The proposed fiber is used as the gain medium of a laser, and the effects of erbium-dopant distribution, erbium-dopant concentration, fiber length, and pump power upon the output mode of the erbium-doped fiber laser are analyzed through numerical investigation. The TE₀₁ or TM₀₁ modes are obtained separately by doping erbium in different annular regions of the proposed fiber, and the slope efficiencies of the proposed fiber laser can reach 67.4% and 63.5%, with an output-mode purity reaching 99.97% and 99.99%, respectively. The proposed anti-parabolic-fiber-based erbium-doped laser has the merits of a high slope efficiency and high mode purity, and has many applications such as in high power lasers, optical-fiber communications, and optical-fiber sensing systems.