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 Gamma-law equation of state with Gamma = 2 and a corotating velocity field as a first step. The mass of the BH is chosen to be approximate to 3.2M(circle dot) or 4.0M(circle dot), and the rest mass of the NS approximate to 1.4M(circle dot) with a relatively large radius of the NS approximate to 13 -14 km. The NS is tidally disrupted near the innermost stable orbit, but similar to 80 -90% of the material is swallowed into the BH and the resulting disc mass is not very large as similar to 0.3M(circle dot) even for a small BH mass similar to 3.2M (circle dot). The result indicates that the system composed of BH and a massive disc of approximate to M-circle dot is not formed from nonspinning BH -NS binaries irrespective of the BH mass, although a disc of mass similar to 0.1M (circle dot) is a possible outcome for this relatively small BH mass range as approximate to 3 -4M(circle dot). Our results indicate that the merger of low-mass BH and NS may form a central engine of short-gamma-ray bursts.