A piecewise alpha function was proposed for the Peng-Robinson equation of state (PR EoS) to predict the thermodynamic properties of pure compounds. The proposed alpha function and its derivations satisfied the requirement of consistency test. The new alpha function with PR EoS was used to predict the vapour pressure of 11 kinds of compounds, and the average relative deviation is 0.34 %. The average relative deviations of the new alpha function for the prediction of liquid volume, enthalpy of vaporization, and isobaric heat capacity of 7 kinds of compounds are 7.54 %, 1.37 %, and 6.90 %. The new alpha function is better than Soave and Stryjek-Vera alpha functions and is as accurate as of the other alpha functions for the prediction of the vapour pressure of pure compounds. The results of enthalpy of vaporization and isobaric heat capacity of the new alpha function are superior to that predicted with the other alpha functions, the deviations of liquid volume of the eight alpha functions are similar. The new alpha function with PR EoS can accurately predict the vapour pressure and enthalpy of vaporization of pure compounds but has great deviations for the prediction of liquid volume and isobaric heat capacity. It is a benefit to improve the predictive accuracy for liquid volume and isobaric heat capacity by modifying the form of PR EoS.