The target detection performance of the locally optimum detector descends in the bad non-Gaussian clutter environment. To deal with this problem, a radar target detection method based on the fractional lower order locally optimum is proposed. First, the simplified locally optimum detector is obtained, then, based on the fractional lower order statistics theory, the fractional lower order correlation matrix expresses the clutter correlation and the fractional lower order quadratic form is proposed as the weight of the locally optimum detector to improve the radar target detection in a non-Gaussian correlated clutter background. Simulations and IPIX radar data results show that, the detection performance of the proposed method obviously outperforms the locally optimum detector in the non-Gaussian badly clutter environment for the weak target.