Incomplete data subject to non-ignorable non-response are often encountered in practice and have a non-identifiability problem. A follow-up sample is randomly selected from the set of non-respondents to avoid the non-identifiability problem and get complete responses. Glynn, Laird, & Rubin analyzed non-ignorable missing data with a follow-up sample under a pattern mixture model. In this article, maximum likelihood estimation of parameters of the categorical missing data is considered with a follow-up sample under a selection model. To estimate the parameters with non-ignorable missing data, the EM algorithm with weighting, proposed by Ibrahim, is used. That is, in the E-step, the weighted mean is calculated using the fractional weights for imputed data. Variances are estimated using the approximated jacknife method. Simulation results are presented to compare the proposed method with previously presented methods.