The nonlinear development of the double-tearing instability and the mode coupling of different helicities are investigated numerically in cylindrical geometry. The results show that double-tearing instability arises with a central-hollow current-density profile, and the coupling of different low-poloidal mode numbers m leads to rapid destabilization of modes with higher poloidal mode numbers. This instability ultimately leads to the resistive reconnection of parts of the fluxes and reduces the current gradient in the unstable region. It seems likely that this process would accelerate current penetration in the tokamak start-up phase, and it also possibly plays an important role in the triggering of solar flares.