In this study, a source scheme based on source biasing as well as discrete energy spectrum in the cylindrical geometry is presented for the simulations of muon tomography in the GEANT4 toolkit. First, a lateral cylindrical surface and a top circular disc act as a generation surface that surrounds the tomographic setup. Then, the generated muons are directed towards the origin where the target volume is situated. Secondly, the kinetic energy of the entering muons is assigned by using a 80-bin discrete energy spectrum between 0 and 8 GeV that is extracted from the CRY muon generator. Thus, the present recipe is called cylindrical oriented muon emission (COME). This source scheme may especially find its applications in the cases where the lateral muon detectors are utilized in order to profit from the horizontal or horizontal-like muons.