Transcendental terms appear in the characteristic equaiton of a power system when time delays of wide area feedback signals are considered.This makes it very difficult to obtain critical system eiganvalues via direct solution of the equation.A method for computation of partial eigenvalues of time-delayed power system is proposed by using Pade rational polynomials to approximate the delay terms.The polynomials are firstly transformed into equivalent state-space representations then balanced.Based on interconnections with the original power system without time delay and the wide area damping controllers，the linear model for the time-delayed power system is established.Finally，sparse eigenvalue algorithms can be used to compute partial eigenvalues of the system according to the sparse characteristics of system coefficient matrices.The method makes it possible to analyze power system small disturbance stability and design wide area damping controller by inheriting the conventional method and theoretical framework of eigenvalue.The eigenvalues and their sensitivities with respect to time delay on both the two-area four-machine and the New England10-machine39-bus test systems demonstrate that the method proposed can accurately compute some eigenvalues relating to system dynamic components.The number of correctly solved eigenvalues corresponding to the time delay and their accuracy strongly relates to the order of the Pade rational polynomial.