The aim of this work is to define a simplified semi-analytical beam transportation code that can calculate the spatial distribution of projectile fragments which are widely distributed in a patient's body during heavy-ion beam radiotherapy. In this code, we employed an elemental pencil beam model where the spatial distribution of radiation quality for an elemental beam is calculated and superposed according to the emittance ellipse of the narrow heavy-ion beam determined at the entrance of the target. The radiation quality for an elemental beam was calculated using Goldhaber's model of fragment distribution. The calculation results were compared with the experimental observations for a mono-energetic narrow (12)C beam measured at the secondary beam line in HIMAC. Despite its simplicity, the developed code could reproduce the experimental results well.