Intensity Diffraction Tomography (IDT) is a label-free computational microscopy technique that infers 3D refractive index (RI) and absorption distributions of objects from intensity-only measurements. Nevertheless, the inherent coherent image formation model requires sequential intensity measurements under various plane-wave illuminations, resulting in time-consuming data acquisition and low imaging speed. In this Letter, we propose Differential Phase Contrast Intensity Diffraction Tomography (DPC-IDT), which leverages partially coherent illumination to extend the accessible spectrum range, thereby achieving high-speed, motion-free 3D tomographic microscopy. DPC-IDT integrates DPC illumination within the IDT framework, allowing 3D RI tomogram reconstruction from only four intensity images under matched asymmetric annular illumination. The effectiveness of DPC-IDT is experimentally validated by RI measurements of standard microspheres. We also demonstrate dynamic 3D imaging results of living PLC cells at 25 Hz volume rate, highlighting its potential for high-speed biological imaging of unstained samples.