Abstarct: An ion source is a device that produces a beam of ions. Ion sources are used in mass spectrometry, isotope separation, nuclear fusion, accelerators, neutron production, ion implantation and ion etching. Many different kinds of ion sources have been developed. one of the most important is the penning or PIG ion source. Due to its simplicity of structure and longer life time, these ion source are more widely considered than other ion sources. Today, all ion sources are simulated before making. In this thesis, the work of simulating the Penning ion source using the CST software is performed and the effect of different factors on the ion of the output of the source is expressed. Among the various structures of the permanent magnet around the source, the Circular arrangement is better for confinement particles inside the source. The best potential for anode, cathode and extraction electrode is 15+, -500 and -3000 volt, respectively. The decelerator and accelerator electrodes are used for transport the output beam from the extraction system. Electrostatic lenses are also used to focus the beam. In the discussion of beam optics and electrostatic lenses, it was more beneficial to focus by the triode system (Einzel lens) than the diode system (immersion lens).