With the rapid popularity of unmanned aerial vehicles (UAVs), airspace safety is facing tougher challenges, especially for the identification of non-cooperative target UAVs. As a vital approach for non-cooperative target identification, radar signal processing has attracted continuous and extensive attention and research. The constant false alarm rate (CFAR) detector is widely used in most current radar systems. However, the detection performance will sharply deteriorate in complex and dynamical environments. In this paper, a novel truncated statistics- and neural network-based CFAR (TSNN-CFAR) algorithm is developed. Specifically, we adopt a right truncated Rayleigh distribution model combined with the characteristics of pattern recognition using a neural network. In the simulation environments of four different backgrounds, the proposed algorithm does not need guard cells and outperforms the traditional mean level (ML) and ordered statistics (OS) CFAR algorithms. Especially in high-density target and clutter edge environments, since utilizing 19 statistics obtained from the numerical calculation of two reference windows as the input characteristics, the TSNN-CFAR algorithm has the best adaptive decision ability, accurate background clutter modeling, stable false alarm regulation property and superior detection performance.