An infrared anomaly target detection algorithm based on a single Gaussian model is a commonly used detection algorithm that can adaptively update the background model. The algorithm performs Gaussian modeling on the output response of each pixel and determines whether the target pixel is a foreground pixel through a defined threshold to realize detection. This paper proposes an improved anomaly detection algorithm based on a single Gaussian model. The algorithm uses the Neiman-Pearson criterion to define the optimal threshold, which overcomes the limitation of selecting the threshold based on empirical values. The paper lays a theoretical foundation for obtaining the best decision threshold so that under a certain false rate, the detection probability can reach the highest value. Experimental results show that, compared to the commonly experienced thresholds, the threshold determined in this study provides a much better detection effect.