We have discovered an unstable periodic solution to the incompressible filtered Navier-Stokes equation for box turbulence driven by the steady external body force. We have obtained the periodic motion by using a Newton-Krylov-hookstep method with a global convergence property. The energy transfer event can be described by the vortex dynamics in the periodic motion at moderate Reynolds number. There are three distinct temporal phases. First, a large amount of energy is injected to the largest scale due to the external forcing; the four largest-scale vortices become vigorous. Secondly, the vortices create strain fields between them; in those fields the smaller-scale vortices are created. In the last phase, most of energy is transferred to the sub-grid scale; vortices at all the scales becomes quiescent. After the quiescence period, the largest-scale vortices start getting vigorous back to the first phase.