During cooling at a rate of 10 degrees C/min from the melt state of PEEK we have followed the growth of spherulites using an optical microscope equipped with a camera. The isothermal growth rates of crystallization in the temperature range of 266-308 degrees C could be estimated by means of a differential equation. These continuous growth rate data were used further for kinetic analysis, which indicated that PEEK exhibited an unmistakable regime II --> III transition at 296 degrees C. The results compared favorably with those obtained by the traditional isothermal method, which is time consuming. Due to chain folding, the Thomas-Staveley constant should be closer to 0.25 instead of 0.1 or 0.3.