The 13-MeV proton linac of the Compact Pulsed Hadron Source (CPHS) at Tsinghua University,China,is composed of a 50-keV electron cyclotron resonance proton source,a 3-MeV four-vane-type radio-frequency quadrupole (RFQ) accelerator,and a drift tube linac (DTL).Precise measurement of the beam energies at the exit of the RFQ and the DTL is critical for DTL commissioning.Two button-type beam position monitors (BPMs) installed downstream of the RFQ are used to perform the measurement using a time-of-flight method.The effects of several factors on phase measurement accuracy are analyzed.The phase measurement accuracy of the BPMs at CPHS is better than ± 1.03° at 325 MHz after corrections,corresponding to an energy measurement error of ± 0.07％.The beam energy measured at the exit of the RFQ is 2.994 ± 0.0022 MeV,which is consistent with the design value.