The nonlinear evolution of the double tearing mode is numerically investigated in 2D geometry. Long and thin current sheets are found to be formed and become tearing unstable in the high Lundquist number regime during the fast reconnection phase, leading to the onset of the secondary and tertiary islands (plasmoids). Eventually the system saturates at a quasi-stationary state with those islands coexisting in two pairs. Interestingly, a new evolution process, characterized by two fast reconnection phases, is also discovered for an intermediate distance between the two resonant surfaces due to the evolution of current ribbons associated with the secondary island. These results are obtained only when the symmetry of magnetic configuration is strictly guaranteed in numerical calculations.