A generalized hyperbolic perturbation procedure is presented to extend the validity of the hyperbolic perturbation method for homoclinic solution of nonlinear oscillatory system (x) + g(x)=εf(μ,x,(x)), in which g(x) is a function of displacement x with arbitrary odd and even nonlinearity and μ is a parameter.The generalized hyperbolic functions are employed to express the homoclinic solution.Critical value of homoclinic bifurcation parameter μ can be determined in the perturbation procedure.To assess the efficiency of the present method, three typical examples are studied in detail.