We have investigated the possibility that magnetic reconnection between oppositely sheared magnetic loops works as a trigger mechanism of solar flares, based on three-dimensional numerical simulations. The simulations were carried out by applying a slow footpoint motion, which reverses a preloaded magnetic shear, in the vicinity of the magnetic neutral line. The simulation results clearly indicated that the reversal of magnetic shear can cause a large-scale eruption of the magnetic arcade through a series of two different kinds of magnetic reconnections. The first reconnection is initiated by the resistive-tearing mode instability growing on the magnetic shear inversion layer and annihilates the sheared magnetic fluxes, which are oppositely directed along the magnetic neutral line. As a result of this, the magnetic arcade collapses into the reconnection point, and a new current sheet is generated above and below the shear inversion layer. The generation of new current sheets is followed by another magnetic reconnection, which drives the eruption of the sheared magnetic arcade. Mutual excitation of the two reconnections may explain the explosive property of the flare onset.