In order to improve the detection performance of constant false alarm detectors in multi-targets environment and effectively control the rise of false alarm rate at the clutter edges, a new CFAR detecting algorithm (OSUMGO-CFAR) is proposed based on efficient unbiased minimum-variance estimation (UMVE). In this algorithm, OS and UMVE methods are respectively adopted to create two local noise power estimations, the maximum value of them is used to set an adaptive detection threshold. Under SwerlingⅡassumption, the analytic expressions of MGF and ADT in homogeneous background are derived , again the analytic expressions of Pd in multi-targets environment and the peak of false alarm rate at clutter edges are derived. With numerical analysis, the CFAR-LOSS and peak of false alarm rate are taken respectively as the measurement of performance in multi-targets environment and at the clutter edges. The analysis results show that the algorithm is better than OSTMGO and GOSGO in performance in non-homogeneous background.