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In this paper, a scheme incorporating the Linstedt-Poncaré (L-P) method and multiple scales method for strongly nonlinear stochastic systems with light fractional damping under random harmonic excitation is developed.General procedure of this method is listed.By introducing time transformation τ =ωt to the strongly nonlinear systems, expanding the frequency ω and adding several new time scales, a series of differential perturbation equations are derived according to the powers of parameter.Solving these perturbation equations and eliminating the secular producing terms leads to a second-order approximate solution of the system.In addition, the steady state frequency amplitude function in deterministic case is obtained, and the first order and second order steady state moments of amplitude are given in stochastic case.Two examples are presented to verify the validity of the procedure, in which comparisons of analytical amplitude frequency responses and Monte Carlo numerical simulations are taken and show good agreement.Specially, the method has a good character to handle some types of nonlinearity like x3 whose intensity could be infinite and discussions follow each example.