Abstract: A new and simple method is proposed for studying an imperfect bifurcation problem of one-dimensional vector field with a time-dependent parameter. A basic method of scaling balance is established. By combining this method with the continuity of the solutions of ordinary differential equations with respect to time and parameters, the delayed bifurcation transition and the influences on the bifurcation diagrams are discussed. Three different types of model bifurcation equations are analyzed concretely, the scaling relations and the intervals of bifurcation transition are given. The qualitative analysis results coincide with the numerical ones. Our studies imply that there exists a critical value of imperfect parameter such that if the imperfect parameter is respectively smaller than, equal to and larger than the critical value, the corresponding time dependent bifurcation is delayed, almost the same as and advanced the steady one respectively.