Dynamic and quantiative observing on the biological samples is important for life and biological sciences research. A digital holographic microscopy for long-term quantitative phase-contrast imaging of living cells is proposed. At the condition that biological cells for microscopic observation are usually in semi-enclosed environment actually, the optical configuration of digital holographic microscopy is designed and optimized by using free-space-fiber hybrid optical structure. Considering the additional phase aberration induced by liquid culture medium in long-term observation, the system aberrations are numerically corrected at the hologram plan and image plan, in order to obtain high quality phase contrast images. The living samples of MC3T3-E1 and MLO-Y4 cells are investigated by long-term microscopic observation, and the experimental results are given to confirm the proposed method.