A new method is presented using a tri-window common-path interferometer (TriWCPI) for quantitative phase measurement. The prior method obtains the phase shift introduced by the Ronchi grating and the intensity value of the incident light with interferograms acquired offline without any objects. As a consequence, an improved recovery algorithm is established using the phase shift, the intensity value of the incident light, and the interferograms for a phase object acquired by camera in a single shot. The phase of an object then can be reconstructed from the improved algorithm. Because the calculation of phase shift and intensity value can be performed offline only once after the TriWCPI is built, the real-time ability and stability of the TriWCPI remains in this method. But the method avoids the normalization process and thus improves phase-retrieval precision. Experiments are demonstrated to prove the precision, real-time ability, and stability of the proposed method.