In this paper, the challenging task of target detection in sea clutter is addressed. We analyze the statistical properties of the signals which have been received from the scene and based on that, we model the amplitude of the signals that have been reflected from the background sea clutter according to several well-known probability distribution functions. Next, by exploiting the Kullback-Leibler (KL) divergence metric as a goodness-of-fit test, we will demonstrate that among the proposed probability distributions, the Weibull distribution can model the statistical properties of the background sea clutter with higher accuracy. Subsequently, we utilize the aforementioned information to design an adaptive threshold based on the Constant False Alarm Rate (CFAR) algorithm to detect the energy of the targets which have been buried in the sea clutter. Thorough analysis of the experimental data gathered from the Canadian RADARSAT-1 satellite demonstrates the overall effectiveness of the proposed method.