In this paper, we put forward a new approach towards realizing measurement-device-independent quantum key distribution with passive heralded single-photon sources. In this approach, both Alice and Bob prepare the parametric down-conversion source, where the heralding photons are labeled according to different types of clicks from the local detectors, and the heralded ones can correspondingly be marked with different tags at the receiver's side. Then one can obtain four sets of data through using only one-intensity of pump light by observing different kinds of clicks of local detectors. By employing the newest formulae to do parameter estimation, we could achieve very precise prediction for the two-single-photon pulse contribution. Furthermore, by carrying out corresponding numerical simulations, we compare the new method with other practical schemes of measurement-device-independent quantum key distribution. We demonstrate that our new proposed passive scheme can exhibit remarkable improvement over the conventional three-intensity decoy-state measurement-device-independent quantum key distribution with either heralded single-photon sources or weak coherent sources. Besides, it does not need intensity modulation and can thus diminish source-error defects existing in several other active decoy-state methods. Therefore, if taking intensity modulating errors into account, our new method will show even more brilliant performance.