This paper describes a numerical study of the magnetic reconnection between two magnetic fields of opposite polarity. The magnetic fields are created by an electric current in a coil connected to two metal disks. One of the disks is irradiated by a strong laser beam, whereby large amounts of free electrons flow toward the other disk, constituting a closed circuit for the electric current flowing through the coil. Two parallel coils are arranged to connect the two disks, and irradiation of the laser beam on one disk results in parallel electric currents in the two coils, inducing two magnetic fields of opposite polarity in the region between them. The magnetic reconnection that occurs in this region is three-dimensional. This three-dimensional magnetic reconnection is investigated via magnetohydrodynamic numerical simulations. The characteristics of the Petschek-type magnetic reconnection are observed for the first time in such numerical simulations of magnetic reconnection. Changes in the shape of the magnetic field lines form the boundary of the dissipation region and the outflow region. Moreover, the thermal plasma generated by reconnection is strongly confined to the region where the reconnecting current sheet and the slow-mode shock are located, and no leaks of thermal plasma are observed. Comparisons with existing laboratory experiment results confirm that our numerical simulations reproduce the experimental outcomes and provide reasonable explanations for the results observed in laboratories.