Data consisting of three different entities (e.g., individual, item, and time) are commonly referred to as three-mode data. The present study focused on three-mode data where one entity is time, namely longitudinal multivariate data collected from the same set of individuals. To identify time trends underlying the three-mode data, a three-mode GMANOVA model was proposed. This model expresses three-mode data by means of a matrix containing explanatory variables for individuals, for items, for a function of time trend and parameters. Although algorithms for estimating the three-mode GMANOVA model have been proposed, the available algorithms require a predefined matrix for explanatory variables to differentiate individuals. However, selecting proper explanatory variables prior to the analysis can be challenging in practice. Thus, the present study proposes an algorithm to select explanatory variables for individuals by means of the group Lasso.