A theoretical study for three level laser systems, describes the interaction process between optical fields and optical fiber material of amplifier. This study gives a simple approach expression for gain coefficient which depends on some parameters such as input power pump rate, number of doped atoms per unit volume, fiber length and core radius. It has been found that In order to keep the fiber amplifiers doped with praseodymium as short as possible with good efficiency, it is best to increasing the doped concentration. For 3m length and doping concentration, the gain is 8dB, while for same length and pump power the gain is >10dB if doping concentration .