In this paper, magnetic reconnection caused by the tearing-mode instability ina long and thin cylindrical geometry is numerically studied in the framework ofthree-dimentional incompresible resistive MHD theory. The results show that thenonlinear coupling of tearing modes with low ploidal mode numbers leads to therapid destabilization of the modes with higher ploidal mode numbers and to fastmagnetic reconnection. Furthermore, tearing mode turbulence is generated and theanomalies will be produced. The anomalous resistivity can quicken the growth ofthe tearing-mode instability and accopanying reconnection process. It is suggestedthat fast magnetic reconnection as a mechanism for the solar flares may be associated with this self-excited process caused by the nonlinear coupling of tearingmode instabilities in the solar corona.