Abstract: The inverse eigenvalue problems of generalized star graph matrices（matrices of a special kind of tree） with degree 2 were studied by using two methods. Firstly, a scheme for labeling the vertices of such a tree was introduced in order to express the corresponding matrices in a number of special forms.Then, inverse eigenvalue problem of matrix for the given two different kinds of eigendata was transformed into the solution of the system of linear equations, and the sufficient and necessary conditions for the problem to have a unique solution were obtained. Finally, an expression for the unique solution of the matrix was provided, and the numerical algorithms and examples were given to verify the accuracy of the results.