This paper reported a general non-interferometric high-accuracy quantitative phase imaging (QPI) method for arbitrary complex-valued objects. Given by a typical 4-f optical configuration as the imaging system, three frames of small-window phase modulation are applied on the object's Fourier spectrum so that redistributed intensity patterns are produced on the image plane, in which the object phase emerges at different degree. Then, an algebraic relationship that connects the object phase with the output intensity is established to provide us with an approximate closed-form phase recovery. Further, an efficient iterative optimization strategy is developed to turn that approximate solution into an accurate one. Due to the linear convergence property of the iteration, a high-accuracy phase recovery is achieved without requiring heavy iterations. The feasibility and accuracy of the proposed method are verified by both numerical simulations and experiments on diverse phase objects including biomedical tissues. © 2021