Quantitative Phase Imaging (QPI) is a technique that can measure the phase map of the light field. It has the characteristics of label-free, non-invasive and three-dimensional observation and has been widely used in bioimaging and industrial inspection. A number of techniques have been developed to measure phase information of objects, including the interferometric method such as Digital Holographic Microscopy (DHM), and the non-interferometric method such as the Fourier Ptychography Microscopy (FPM), Transport of Intensity Equation (TIE) method and so on. The interferometric method has high measurement accuracy but a complex experimental setup sensitive to the environmental disturbance. The non-interferometric method recovers phase from the intensity patterns of objects, but requires iterative calculation or multiple images recorded at different positions, which makes the imaging speed slow and unsuitable for real-time observation. The quantitative phase imaging based on Quadriwave Lateral Shearing Interferometry (QLSI) has the advantages of the referenceless beam, simple configuration, high stability and fast imaging speed. In the existing studies, Cross Grating (CG), Modified Hartmann Mask (MHM), Randomly Encoded Hybrid Grating (REHG) and other splitter elements were used for QLSI. The cross grating has low diffraction efficiency and energy utilization rate (~10%) for the four beams of first-order diffraction. The MHM and REHG can concentrate the diffracted light energy on the four first-order diffraction beams. But the MHM still has a low energy utilization rate (~37%), and the REHG has a complex structure for fabrication.This paper proposes a quantitative phase imaging method based on QLSI using a two-dimensional (2D) Ronchi phase grating. The light incident to the 2D Ronchi phase grating is diffracted mainly with energy concentrated on the four first-order diffraction beams, occupying 65.7% of the total incident energy. The object light carrying the sample's phase information is imprinted to the 2D Ronchi phase grating and then copied into four beams, which interfere with each other to produce the quadriwave lateral shearing interferogram. The quantitative phase image of the sample is reconstructed by Fourier analysis of the interferogram. The influence of the grating period on the QLSI imaging is analyzed theoretically, and the optimal grating period is determined to be six times of the pixel size of the detector. This match can make the best use of the spatial bandwidth product of detector and achieve high resolution image. The influence of the illumination wavelength on the phase reconstruction is theoretically analyzed, which shows that the proposed method is insensitive to the illumination wavelength. The feasibility of quantitative phase imaging under wide spectral light illumination source is demonstrated. The compact QLSI module is constructed with the pixel size of 9 μm×9 μm of the detector and the period of 54 μm of the 2D Ronchi grating. The grating period is precisely six times of the pixel size, meeting the requirement of the optimal condition. The QLSI module is directly connected to a conventional optical microscope to implement the QPI imaging of e.g., Polymethyl Methacrylate (PMMA) microspheres, microlens arrays and staphylococcus section. The relative error of phase experimentally measured is about 1.8%, proving that the method has a high precision of phase measurement. The experimental results also show that the method can be used for quantitative phase imaging with a wide-spectrum light source, making it easily combined with conventional optical microscopes to have a great application potential in biomedicine, three-dimensional topography measurement and other related fields.