Abstract: The third-order moments and bispectrum play important roles in analyzing nonlinear time series models. Unfortunately, the explicit expressions for the third-order moments and bispectrum can’t be obtained for general bilinear time series models. Therefore, the approximate formulas of them have to be considered in practice. For the diagonal bilinear time series, a useful method is proposed to evalute the third-order moments and bispectral density. Simulation study verifies the validity of our method.