To the conditional maximum likelihood identification problem of an affine structure under missing data, a permutation matrix is used to divide a random vector into observed and missing parts. Then conditional mean and covariance under missing data are set up to obtain a conditional likelihood function. In the theory, expressions of the derivatives about the conditional maximum likelihood function on the unknown parameter vector, unknown white noise variance and missing data are derived. A separable optimum algorithm is given to be applied in engineering. Finally, simulation results show the effectiveness of the identification method.