The problem of constant false alarm rate(CFAR) detection under Pearson distribution clutter is studied in this paper.We derive the exact elementary expressions of probability of false alarm for cell averaging(CA)-CFAR,greatest of(GO)-CFAR and smallest of(SO)-CFAR in homogenous background,and prove that these detectors are also of CFAR.The performance of these detectors are evaluated both in homogeneous and non-homogeneous clutter.The results show that the SO-CFAR has the best detection performance against uniform clutter background and multiple target environments,while the GO-CFAR has the best control ability of false alarm against clutter edges.