A Support Vector Machine (SVM) with the auto-correlation of compactly supported wavelet as kernel is proposed in this paper. It is proved that this kernel is an admissible support vector kernel. The main advantage of the auto-correlation of a compactly supported wavelet is that it satisfies the translation invariant property, which is very important for signal processing. Also, we can choose a better wavelet from different choices of wavelet families for our auto-correlation wavelet kernel. Experiments on signal regression show that this method is better than the existing SVM function regression with the scalar wavelet kernel, the Gaussian kernel, and the exponential radial basis function kernel. It can be easily extended to other applications such as pattern recognition by using this newly developed auto-correlation wavelet SVM.