It is shown that a laser by using the relativistic Doppler effects of high energy ion beam in negative temperature state will be continuously turnable from infrared to X-ray region. The turnability range is △νT=2ν0βγ. The relativistic fransform of the laser parameters are given, and the gain, threshold" and output parameters of the relativistic ion beam laser are calculated in the present work. The methods to excite ion beam by means of laser are analysed. The design of He+ and Ar+ ion beam lasers are also discussed.