Abstract: The delay differential equation is first changed to be an integral equation. The corresponding difference equation is obtained by the discrete integral equation. The relation between the eigenvalues of the discrete difference and the delay differential equation is presented analytically. It yields that a new approximate method is proposed to calculate eigenvalues of the delayed differential equation. As an example, the first ten-order eigenvalues are computed for an delayed Logistic equation. The results with the error estimation show the present method provides not only simple steps but also high accuracy.