Abstract: This paper looks into some properties of eigenvalues to Jacobi operators with a special class of boundary conditions. A few methods for treating the Sturm-Liouville operators are adopted for processing the Jacobi operators with a special class of boundary value conditions. And through the investigation of the properties of eigenvalues to Jacobi operators with a special class of boundary value conditions and through strict mathematical proof, the conclusion is reached that the Eigenvalues to the Jacobi operators with a special class of boundary value conditions are found to have continuous dependence on their coefficients.