This paper aimes at the automatic target detection of ground penetrating radar in goaf area of the power transmission corridor complex underground environment. A generalized likelihood ratio test (GLRT) of target’s hyperbolic characteristic is proposed. In this method, the spherically invariant random process is used to describe the non-Gaussian clutter background. The hyperbola is tested as a whole to be decided whether it is originated from a target or not. So the target characteristic and the statistical properties are fully utilized to enhance the signal to clutter/noise ratio gain. Furthermore, an approximated GLRT is derived to simplify computation under the premise in detection performance. The approximated GLRT is insensitive to the distribution type of clutter, and in consequences, is of great engineering value. Experiments and the results analysis verify the performance of the proposed methods.