We consider the convergence problem of an inexact Cayley transform method for solving inverse eigenvalue problems with multiple eigenvalues. Under the nonsingularity assumption of the relative generalized Jacobian matrix at the solution C∗, a convergence analysis covering both the distinct and multiple eigenvalues cases is provided and the superlinear convergence is proved. Moreover, numerical experiments are given in the last section and comparisons with the Cayley transform method are made.