本文主要研究对称随机矩阵的逆特征值问题。通过将该问题转化为求两个集合交点的可行性问题，提出用交替投影法进行求解。因为其中一个集合不是凸集，关于凸可行性问题的收敛性结果不能用来分析算法的收敛性。对于算法的收敛性，本文在已有关于两个黎曼流形的交替投影算法收敛性的研究结果上，建立了交替投影算法在一定条件下的线性收敛性。最后数值例子也表明了算法的有效性。 The symmetric stochastic inverse eigenvalue problem (StIEP) is considered. By reformulating it into a feasibility problem of two sets, the alternating method is proposed for solving it. Since one of the sets is not convex, the convergence analysis technique for the convex cases does not work. For the convergence of the algorithm, this paper establishes the linear convergence of the alternating projection algorithm under certain conditions on the existing results on the convergence of the alternating projection algorithms for two Riemannian manifolds. At last, some numerical experiments are provided to illustrate the efficiency of the method.