In accordance with the need of observing and analyzing living cells, based on the pre-magnification off-axis digital holographic theory, an inverted setup of pre-magnification off-axis image plane digital holographic microscopy is designed and built, where the image plane of the microscope objective is coplanar with the recording plane of the hologram. Therefore, the step of the numerical diffraction propagation by the computer is needless and the numerical reconstruction is simplified. Meanwhile, the simple and fast surface fit method is applied to correct the phase aberration. Furthermore, the actual resolution is measured by using the USAF resolution mask, which is 0.87 μm. Finally, the quantitative phase-contrast images of the living hippocampal neuron cells in the natural state are achieved. From the experimental results, the structures of cells including the cell body and the dendrite are observed. The basic parameters of the cell morphology are also obtained. The results show that the digital holography is useful in the quantitative morphological detection of living cells and it provides a non-destructive phase-contrast imaging approach for the cell morphological analysis in the field of the bio-medical research.