Hydraulic fracturing becomes more difficult when confronted with a formation of high fracturing pressure. In such formations, acidizing before the main fracturing treatment provide a method to reduce fracture pressure. The aim of this paper was to investigate the evolution of fracture pressure in a wellbore with acidizing. Five experiments were conducted to study the mechanisms of acid damage on reservoir minerals and cementing materials properties. Consequently, a mathematical model to predict fracture pressure with acidizing has been established and verified by field data. The analysis results showed that it is possible to reduce fracture pressure with decreased rock strength and fracture critical stress intensity factor by means of acid damage. Acid damage destroys the crystal structure of mineral particles, breaks the crystalline layers in cementing materials, increases rock porosity and reduces the rock strength. In addition, as the acid concentration, formation temperature and acid treatment time increased, it was useful to reduce fracture pressure in the wellbore. Using the proposed model, we were able to select the optimal acid damage construction parameters to reduce fracture pressure.