A multi-strategy switching variability index CFAR (MSVI-CFAR) detector is proposed to further the capability of radar target constant false alarm detection in complex backgrounds. The detector can estimate the clutter background in the reference window. It adaptively selects the optimal detection strategy from the cell-averaging CFAR (CA-CFAR), greatest-of CFAR (GO-CFAR), switching CFAR (S-CFAR), and ordered statistic with cell averaging CFAR (OSCA-CFAR). The results indicate that MSVI-CFAR is beneficial to the detection of SVI-CFAR in the background of uniform background, clutter edge, and multi-target interference and has less CFAR loss and more robust anti-multi-target interference performance.