A method based on the nolinear Granger causality is used to analyze sleep physiological signal. Polynomial kernel function, Gaussian kernel function and sigmoid kernel function are used to map the linear data in low dimensional input space into high dimensional feature space in which linear Granger method can be used to analyse the biomedical signals. The analysis results show that the causal effect of electrocardlogram (ECG) signals to electroencephalogram (EEG) signals, ECG signals to blood pressure signals and blood pressure signals to ECG signals are more significant than that of the opposite direction. In addition, the results of sleep subjects have more significant difference than that of normal subjects. The simulation results validate that the sleep physiological signal reflects the causality more objectively.