Spectrum aliasing in off-axis digital holography may result in poor image reconstruction quality. This study proposes a method to eliminate the zero-order spectrum and enhance image quality based on Kramers-Kronig relations and phase background fitting. The Kramers-Kronig relations are employed to derive the quotient of the complex wavefront of object and the reference beam, and phase background fitting is performed in a compensatory way to yield the object complex wavefront. The effectiveness of the proposed approach is validated via simulations and experiments. The results show significantly improved off-axis digital holographic microscopy reconstruction quality, making the proposed method a promising option for holographic microscopy imaging.