An electromagnetic launcher (EML) system accelerates and launches a projectile by converting electric energy into kinetic energy. There are two types of EML systems under development: the rail gun and the coil gun. A railgun comprises a pair of parallel conducting rails, along which a sliding armature is accelerated by the electromagnetic effects of a current that flows down one rail, into the armature and then back along the other rail, but the high mechanical friction between the projectile and the rail can damage the projectile. A coil gun launches the projectile by the attractive magnetic force of the electromagnetic coil. A higher projectile muzzle velocity needs multiple stages of electromagnetic coils, which makes the coil gun EML system longer. As a result, the installation cost of a coil gun EML system is very high due to the large installation site needed for the EML. We present a coil gun EML system that has a new structure and arrangement for multiple electromagnetic coils to reduce the length of the system. A mathematical model of the proposed coil gun EML system is developed in order to calculate the magnetic field and forces, and to simulate the muzzle velocity of a projectile by driving and switching the electric current into multiple stages of electromagnetic coils. Using the proposed design, the length of the coil gun EML system is shortened by 31% compared with a conventional coil gun system while satisfying a target projectile muzzle velocity of over 100 m/s.