A kind of new classical-quantum correspondence principle is proposed using the idea of closed-orbit theory. The quantum spectrum function is introduced by means of the eigenvalues and the eigenfunctions in the system of one-dimensional nano-microstructure. The Fourier transformation of the quantum spectrum function is found corresponding with the classical orbits in the system. These results give new evidence about the classical-quantum correspondence. All the methods and results can be used in a lot of other systems, including some two-dimensional and three-dimensional systems. The researches about these systems are very important in the field of applied science, for example, molecular reaction dynamics and quantum information.