The variational method is applied to a single-mode stochastic nonlinear optical system and the dependence of its relaxation rate and spectral amplification factor on the noise intensity based on the linear response theory is investigated.The investigation shows that when the biased input is vanishing,the relaxation rate has different dependence in monostable and multistable cases.The investigation also shows that the stochastic resonance occurs in one-dimensional symmetric monostable potential,and the possible condition for it is pointed out.