In this paper, we study the inverse matrix eigenvalue problem, which has important applications in engineering computation and other fields. The inverse eigenvalue problem is proposed for two given eigenpairs under the premise that the eigenvalues and eigenvectors are known. The inverse N-type matrix eigenvalue problem is studied for a class of inverse tridiagonal matrix variations, and the conditions for the existence of uniqueness of its solutions are proved constructively by discussing the cases, and the algorithm and expressions for the inverse matrix elements are obtained. The effectiveness of the algorithm is verified by numerical examples.