The problem of detecting a weak target in dynamic clutter scenarios is analyzed with a polarimetric high-resolution radar. The heavy-tailed clutter is modeled by the compound-Gaussian process with inverse Gamma distributed texture. With training data to estimate covariance matrix of clutter, an adaptive polarimetric detector based on generalized likelihood ratio test criterion is presented for this heavy-tailed compound-Gaussian clutter. Then, the analytic expression of false alarm is derived to prove its constant false alarm rate property with respect to the clutter covariance matrix. The simulation results confirm the effectiveness of the proposed detector.