Hyperspectral target detection is a great deal of attention in the field of remote sensing signal processing. The KRX algorithm based on kernel machine learning can make full use of nonlinear spectral characteristics among hyperspectral bands. Therefore，it can get better detection results in the original spectral feature space. Aimed at the defect that the complexities of KRX algorithm is high in calculating the detection process and unable meet the requirement of rapid processing. A real-time anomaly detection method is proposed based on recursive kernel function. The recursive thought of Kalman filter is introduced, which puts forward a nuclear recursive hyperspectral anomaly target detection algorithm. From the perspective of spectral analysis, with Woodbury′s lemma, the kernel matrices can be updated by the kernel matrices of last pixel. It avoids repeat computation of high-dimensional data matrices. Experimental results show that the accuracy of anomaly detection is improved and testing time of the algorithm is reduced at the same time when compared with the traditional RX, causal RX and KRX algorithm.