We present our latest results of simulation for merger of black hole (BH)–neutron star (NS) binaries in full general relativity which is performed preparing a quasicircular state as the initial condition. The BH is modelled by a moving puncture with no spin and the NS by the Γ-law equation of state with Γ = 2 and a corotating velocity field as a first step. The mass of the BH is chosen to be ≈3.2M or 4.0M, and the rest mass of the NS ≈1.4M with a relatively large radius of the NS ≈13–14 km. The NS is tidally disrupted near the innermost stable orbit, but ~80–90% of the material is swallowed into the BH and the resulting disc mass is not very large as ~0.3M even for a small BH mass ~3.2M. The result indicates that the system composed of BH and a massive disc of ~M is not formed from nonspinning BH–NS binaries irrespective of the BH mass, although a disc of mass ~0.1M is a possible outcome for this relatively small BH mass range as ~3–4M. Our results indicate that the merger of low-mass BH and NS may form a central engine of short-gamma-ray bursts.