Over the course of the third observing run of the LIGO–Virgo–KAGRA Collaboration, several gravitational-wave (GW) neutron star–black hole (NSBH) candidates have been announced. By assuming that these candidates are real signals with astrophysical origins, we analyze the population properties of the mass and spin distributions for GW NSBH mergers. We find that the primary BH mass distribution of NSBH systems, whose shape is consistent with that inferred from the GW binary BH (BBH) primaries, can be well described as a power law with an index of plus a high-mass Gaussian component peaking at . The NS mass spectrum could be shaped as a nearly flat distribution between ∼1.0 and 2.1 M ⊙. The constrained NS maximum mass agrees with that inferred from NSs in our Galaxy. If GW190814 and GW200210 are NSBH mergers, the posterior results of the NS maximum mass would be always larger than ∼2.5 M ⊙ and significantly deviate from that inferred in Galactic NSs. The effective inspiral spin and effective precession spin of GW NSBH mergers are measured to potentially have near-zero distributions. The negligible spins for GW NSBH mergers imply that most events in the universe should be plunging events, which support the standard isolated formation channel of NSBH binaries. More NSBH mergers to be discovered in the fourth observing run would help to more precisely model the population properties of cosmological NSBH mergers.