An anhydrite (CaSO4) natural sample was studied as possible dosimeter for low and high gamma doses using the technique of electron paramagnetic resonance (EPR). EPR spectrum showed signals due to (SO3)(-), (SO4)(-) radicals and O center. The anhydrite sample was irradiated with gamma rays with low-dose ranges typical for medical therapy (1-20 Gy) up to high-dose of about 70 kGy. The EPR centers due to (SO3)(-) and (SO4)(-) exhibited a linear dose response in the dose range from 1 Gy to 500 Gy, whilst the 0 center presented a supra-linear dose response in the range of 50 to 5 kGy.