The regularized phase tracker (RPT) is one of the most powerful approaches for demodulation of a single fringe pattern. However, two disadvantages limit the applications of the RPT in practice. One is the necessity of a normalized fringe pattern as input and the other is the sensitivity to critical points. To overcome these two disadvantages, a generalized regularized phase tracker (GRPT) is presented. The GRPT is characterized by two novel improvements. First, a general local fringe model that includes a linear background, a linear modulation and a quadratic phase is adopted in the proposed enhanced cost function. Second, the number of iterations in the optimization process is proposed as a comprehensive measure of fringe quality and used to guide the demodulation path. With these two improvements, the GRPT can directly demodulate a single fringe pattern without any pre-processing and post-processing and successfully get rid of the problem of the sensitivity to critical points. Simulation and experimental results are presented to demonstrate the effectiveness and robustness of the GRPT.