The present paper applies the spontaneous fast reconnection model to the three-dimensional (3-D) plasmoid dynamics by extending our 2-D plasmoid study in the (x,y) plane [Ugai, 1995b> to the z (dawn-dusk) direction. As the fast reconnection spontaneously develops, a large-scale plasmoid evolves and propagates through a long current sheet system. There is a large-scale vortex plasma flow around the plasmoid, so that the resulting plasmoid is significantly confined in a limited inner region (in the z direction) because of the converging flow toward the central z=0 (i.e., (x,y)) plane in the backward of the plasmoid. Along the resulting plasmoid boundary layer, slow shocks and finite amplitude intermediate waves simultaneously stand. A (pure) finite amplitude intermediate wave stands just ahead of the slow shock, so that there is a good correlation between the sheared field and flow components Bz and uz. The initial (one-dimensional) sheet current is drastically disrupted in the inner fast reconnection and plasmoid regions, and the current flowing into the inner region is largely bifurcated and concentrated into the slow shock and plasmoid boundary layers. The 3-D plasmoid structure is so complicated that the Bz (dawn-dusk) field component may have a monopolar-like or bipolar-like change depending on the path through which the plasmoid is observed in the x direction. It is proposed that the spontaneous fast reconnection model can reasonably be applied to substorms. ¿ 1998 American Geophysical Union