We develop the fast-Fourier-transformation path-integral approach to investigate the quantum decay of a nonlinear dissipative system. The action of the bounce trajectory, i.e. the exponential factor of decay rate, is obtained. In the case of the nonlinear coupling f(x)=tanh［λ(x-xb)］ between the system and its environment, we find that the nonlinear coupling suppresses the decay rate. In contrast to the usual linear coupling, the action will not abide by the law SB=a［1-b(T/Tc)2］ and the crossover temperature rebounds, which means that the system steps into the quantum tunneling region at a higher temperature.