In this paper,the RKNd method with FSAL technic is considered for oscillatory problems.Since the exponential fitting method is quite necessary for the case that the solutions of the differential systems can be expressed as linear conbinations of functions from the set {exp(λt),exp(-λt)|λ ∈ C} or {sin(ωt),cos(ωt)|λ =iω,i2 =-1,ω ∈ R},we propose an exponential fitting RKNd method with FSAL technic for solving oscillatory problems.Numerical experiments show that the method is more efficiency and competent than some existing RKNd methods.