As to the unknown target detection for polarimetric radars under the background of non-Gaussian clutter, a measurement model of the fully-polarimetric radar with variable transmit and receive polarization is built. Then by employing the generalized likelihood ratio test (GLRT), a novel polarimetric detector based on joint transmit and receive polarization optimization is proposed and the close form of the test statistics is obtained. Furthermore, in the stage of performance analysis, its analytical expression of detection performance is derived. Remarkably, the newly proposed detector has the constant false alarm rate (CFAR) property. Moreover, the correspondence between the polarization vector and the detection performance is clarified. Finally, in the stage of performance assessment, we firstly design the experiment of the unknown target detection under the non-Gaussian clutter background. The results show that, with the same experimental conditions, the proposed algorithm has a better performance against non-Gaussian clutter than the existing polarization detectors for unknown targets, and also a better detection performance than them, while the detection performance of the proposed detector is close to the optimal polarization detector (OPD), which is with a prior knowledge of the target and clutter. Then we compare the detection performances of the polarimetric radar with joint transmit and receive polarization optimization, the one with only transmit polarization optimization and the one with fixed transmit and receive polarizations. The results show that under the same experimental conditions, the detection performance of the aforementioned first radar system is better than the latter two systems.