In order to improve the measurement accuracy, a kind of phase shifting digital holographic microscopy based on a long working distance microscopic objective is proposed. In the setup, an LED is adopted as the illumination light source, which can suppress coherent noise effectively and hence improve the measurement accuracy. A michelson quasi-common-path interferometer is constructed by adding a beam-splitter between the long working distance objective and the sample. The layout of the setup is simple and it can be easily adjusted, and thus the interference can be come into being conveniently especially when the sample is illuminated with a partial light source. The blind phase-shifting interferometry is adopted in the reconstruction procedure, and the two-step blind phase-shifting algorithm is used to reconstruct the phase map of the measured sample. In the experiments, the height maps of a reflective USAF 1951 resolution target are measured under LED illumination and He-Ne laser illumination, respectively. The measurement results show that both coincide with each other; the phase noise under LED illumination is, however, reduced by 70% when compared with that under laser illumination. In addition, in order to further verify the effectiveness of the device, the device is used to measure a micro-nano rectangular step engraved on the silicon substrate. The measurement results are in good agreement with the nominal values. This technique can be potentially used in the topographic measurement of micro-structures.