The primary standard for X-ray dosimetry is based on the free-air ionization chamber (FAC). Therefore, the Atomic Energy Organization of Iran (AEOI) designed the free-air ionization chamber, FAC-IR-۱۵۰, for low and medium energy X-ray dosimetry. The purpose of this work is the study of the free-air ionization chamber characteristics and the design of the FAC-IR-۱۵۰. The FAC-IR-۱۵۰ dosimeter has two parallel plates, a high voltage plate and a collector plate. A guard electrode surrounds the collector and is separated by an air gap. A group of guard strips is used between up and down electrodes to produce a uniform electric field in all the ion chamber volume. This design involves introducing the correction factors and determining the exact dimensions of the ionization chamber by using Monte Carlo simulation.