The method by measuring one photon of an entangled two-photon pair to simultaneously herald another photon as the single photon, is one of the important ways to prepare the desired single-photon source. However, achieving high herald efficiency is still an open problem. In this paper, with the polarization entangled photon pairs generated by the parametric down-conversion process in the I-type phase-matched BBO (β-BaB₂O₄) nonlinear crystal, we investigate how the herald efficiency of the single-photon along the ideal path depends on the selection of the heralded basis of the photon in the signal path. An extended Hanbury-Brown-Twiss experimental system is built with a fiber polarizing beam splitter and three single-photon detectors, to experimentally measure the herald efficiency of the heralded single-photon source. Our results show that with the present polarization entangled-photon system whose quality is relatively low, the herald efficiency with the $|+/-\rangle$ heralded basis is enhanced 4% compared with that with the $|H/V\rangle$ heralded basis.