A method for clustering incomplete longitudinal data, and gene expression time course data in particular, is presented. Specifically, an existing method that utilizes mixtures of multivariate Gaussian distributions with modified Cholesky-decomposed covariance structure is extended to accommodate incomplete data. Parameter estimation is carried out in a fashion that is similar to an expectation-maximization algorithm. We focus on the particular application of clustering incomplete gene expression time course data. In this application, our approach gives good clustering performance when compared to the results when there is no missing data. Possible extensions of this work are also suggested.