We propose a sub-ignition/burning reactor which is named the Laser-fusion Subcritical Power Reactor Engineering Method (L-Supreme). The reliabilities of L-Supreme in a MW class laser facility are assessed with respect to the following points: a reactor core, a target chamber, a target delivery system, an Exhaust Detritiation System (EDS), and neutron shielding. The Japan Establishment for Power-laser Community Harvest (J-EPoCH) would be applied as a MW class laser facility. A non-cryogenic glass balloon target filled with gaseous deuterium-tritium (DT) is contained in a target capsule. A chain-type magazine system might be used for a mass supply of the target capsules. Each target capsule is delivered to the center of a reactor core at 1 Hz. A batch of 10000 laser shots would realize 0.22 MJ fusion power. The amount of tritium per batch is 1.51 x 1012 Bq. During laser experiments, unburned tritium is evacuated and transferred into an Exhaust Detritiation System (EDS). An evacuation rate of more than 0.1 m3/s is required in order to recover less than 5000 Bq/m3 of the threshold of tritium concentration within one hour. For safety, emergency situations such as tritium leakage in facilities are examined. The EDS works by internal circulation processes. Assuming leakage of tritium for a batch, an air circulation flow rate of 4100 Nm3/h is required in an experimental hall for recovering less than 5000 Bq/m3 within 48 hours. A primary and secondary neutron shield concept are proposed and would provide full neutron shielding. We conclude that it is possible to construct the L-Supreme system by marshalling current technologies.