In laser-driven inertial confinement fusion experiments, the CR-39 detector, a commonly-used recording medium for proton energy spectrum diagnosis, has timeliness and consistency flaws in energy spectrum measurement. However, the Timepix detector with the ability to obtain online signals can overcome these problems. To apply the Timepix detector to detect implosion proton energy spectra, it is essential to study the response of the Timepix detector to proton energies and incident angles. This work analyzes the response of the Timepix detector to proton beams in different energies and incident angles within the Allpix² framework using Monte Carlo methods. The simulation results show that the response of the Timepix detector to proton beams in different energies and incident angles exhibits significant differences in cluster morphology, cluster size distribution, and cluster charge distribution. When incident proton beam energy is below 6 MeV, the Timepix detector exhibits high detection efficiency, and the angle of proton incidence does not significantly affect the energy response of the detector.