Regenerative chatter is the most important factor affecting the stability of the milling process. It is core for suppressing chatter and improving production efficiency to accurately and efficiently identify the stable region of milling chatter. For this reason, according to the theory of predictor-corrector, a series of new judgment methods are suggested to obtain the milling stability region by respectively applying the fourth-order Adams-Bashforth-Moulton formula, the fourth-order Simpson formula, and the fourth-order Hamming formula. These presented methods are named as the linear multi-step predictor-corrector method (PCM). Firstly, when the regenerative chatter milling process is described as a second-order time-delay differential equation (DDE) with periodic coefficients which are a function of the tooth passing period, the part of forced vibration in this period is uniformly discretized as a time node set. Secondly, after the fourth-order Adams-Bashforth formula is used to predict the displacement at every time node, the fourth-order Adams-Moulton formula can be employed to correct this predicted value in addition to the fourth-order Simpson formula and the fourth-order Hamming formula. Thus, a higher precision discrete prediction-correction expansion is constructed for the inhomogeneous terms of DDE so that the state transition express can be further obtained for the milling process or milling system. And then, the Floquet theory is depended on to present the judgment criterion of milling stability that the relationship between the spectral radius of the state transition matrix and one. Finally, under the same milling process parameters, comparisons of both the stability lobe curve and the local discrete error curve show that the PCM has a faster convergence rate than first-order semi-discretization method (1st-SDM), and second-order full-discretization method (2nd-FDM). This shows that the PCM can obtain better computational accuracy under the same discrete number whereas the PCM is significantly higher computational efficiency over 1st-SDM and 2nd-FDM.