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.