Optical diffraction tomography (ODT) is an emerging microscopy that enables quantitatively three-dimensional (3D) refractive index (RI) mapping of subcellular structure inside biological cells without staining. Due to the noninvasive, label-free, and quantitative imaging capability, ODT has become an important technique in the fields of cell biology, biophysics, hematology, and so on. It is customary to acquire a set of two-dimensional (2D) phase images of a transparent sample from different illumination angles by using the classical Mach-Zehnder interferometry (MZI), and then numerically reconstruct the 3D RI distribution of the sample via appropriate tomographic algorithms. However, due to the limited stability of MZI, the cumulative measured phase errors reduce the accuracy of the reconstructed RI. Here, we propose a common-path ODT based on quadriwave lateral shearing interferometry (QLSI), referred as Q-ODT. In QLSI, the object beam carrying the phase information of sample is divided into four copies by a specially designed 2D diffraction optical element, then the diffracted waves interfere with each other to form the interferogram at the image plane. The complex amplitude map of the object is quantitatively retrieved from the single-shot interferogram by using a Fourier analysis algorithm and a 2D phase gradient integration. A spatial light modulator is employed to ensure high-precision illumination angle scanning without mechanical motion by addressing a series of different periods and orientations blazed gratings. The average fluctuation of the measured phases of a test polystyrene bead by acquiring 300 interferograms in 12 s presents 7.6 mrad, surpassing the conventional MZI-based ODT. The 3D RI distribution of the bead reconstructed from 145 complex amplitude maps via multi-illumination angles with a maximum angle of 70° matches the manufacturer's specification well, demonstrating the high accuracy of the 3D RI imaging capability of the Q-ODT. The lateral and axial resolutions of the 3D RI reconstruction were measured to be 306 ± 21 nm and 825 ± 34 nm, respectively. The proposed Q-ODT method successfully reconstructed the intracellular structure of the biological specimens of Eudorina elegans and mouse bone mesenchymal stem cells (BMSC). The Q-ODT offers a new route towards 3D RI imaging for label-free transparent samples in biomedical research. © 2024 Elsevier Ltd