Chemical shift encoded (CSE)-MRI enables quantification of proton-density fat fraction (PDFF) as a biomarker of liver fat content. However, conventional 3D Cartesian CSE-MRI methods require breath-holding. A motion-robust 2D Cartesian sequential method addresses this limitation but suffers from low SNR. In this work, a novel free breathing 2D Cartesian sequential CSE-MRI method using a variable flip angle approach with centric phase encoding (VFA-centric) is developed to achieve fat quantification with low bias, high SNR, and minimal blurring. Numerical simulation was performed for variable flip angle schedule design and preliminary evaluation of VFA-centric method, along with several alternative flip angle designs. Phantom, adults (n = 8), and children (n = 27) were imaged at 3T. Multi-echo images were acquired and PDFF maps were estimated. PDFF standard deviation was used as a surrogate for SNR. In both simulation and phantom experiments, the VFA-centric method enabled higher SNR imaging with minimal bias and blurring artifacts. High correlation (slope = 1.00, intercept = 0.04, = 0.998) was observed in vivo between the proposed VFA-centric method obtained PDFF and reference PDFF (free breathing low-flip angle 2D sequential acquisition). Further, the proposed VFA-centric method (PDFF standard deviation = 1.5%) had a better SNR performance than the reference acquisition (PDFF standard deviation = 3.3%) with P<.001. The proposed free breathing 2D Cartesian sequential CSE-MRI method with variable flip angle approach and centric-ordered phase encoding achieved motion robustness, low bias, high SNR compared to previous 2D sequential methods, and low blurring in liver fat quantification.