In order to eliminate a large amount of speckle noise and parasitic interference fringes noise caused by high coherence light source (laser), as well as the effects from the mechanical vibrations and air fluctuations which typically affect any uncommon-path interferometric system, we design and establish a white-light (halogen-light) common-path digital holographic microscope based on the grating diffraction. First, the parameters of the selected optical elements and the optical system are derived by theoretical analysis and calculation. Then, a common-path off-axis digital holographic microscope based on grating diffraction, which uses a halogen lamp as the illumination light source, is constructed. At last, the imaging accuracy and the spatiotemporal noise of the system are measured. Experimental results demonstrate that the established digital holographic microscope has a very high accurate imaging performance and spatiotemporal sensitivity with the spatial noise of 0.6 nm and the temporal noise of 0.04 nm.