A time-split transport scheme has been developed for the high-order multiscale atmospheric model (HOMAM). The spacial discretization of HOMAM is based on the discontinuous Galerkin method, combining the 2D horizontal elements on the cubed-sphere surface and 1D vertical elements in a terrain-following height-based coordinate. The accuracy of the time-splitting scheme is tested with a set of new benchmark 3D advection problems. The split time-integrators are based on the Strang-type operator-split method. The convergence of standard error norms shows a second-order accuracy with the smooth scalar field, irrespective of a particular time- integrator. The results with the split scheme is comparable with that of the established models.