A setup of the lensless Fourier transform digital holography is built to get the quantitative high-fidelity phase-contrast images of the biological samples. The basic advantage of such system is that the numerical reconstruction is directly applying only once fast Fourier transform to the intensity distribution of the hologram. However, the aberration appears in the phase image obtained by this kind of reconstruction algorithm and degrades the quality of the phase image seriously. Then, two-step subtraction method is applied to correct the phase aberration. In the experiments, at first two biological sample-plates for teaching are used as the objects, which are the mouse of the skeeter and the epidermal cells of the onion respectively. Then the living free-of-marker cervical carvinoma cells are presented as the object. Not only the clear morphologies of the static biological samples, but also the dynamic variations of the living cells are observed. The experimental results verify the validity of the digital holographic microscopy for the quantitative phase-contrast imaging of the biological samples.