Traditional direction-of-arrival (DOA) estimation methods often encounter challenges such as low accuracy and high computational complexity, particularly in complex signal environments with multiple sources. To address these issues, this paper proposes a fast DOA estimation method for improper Gaussian signaling (IGS) non-circular signals, based on a coprime array; this approach involves extending the array model by leveraging the unique properties of non-circular signals. Subsequently, this study introduces the ANCM algorithm, a method designed for fast DOA estimation of IGS non-circular signals within a non-uniform noise background. The proposed ANCM algorithm is then compared to classical algorithms, through simulations in a non-uniform noise environment. Experimental results demonstrate that the ANCM algorithm significantly outperforms traditional methods in such conditions. Therefore, the development of new, efficient DOA estimation methods holds substantial theoretical and practical value.