This paper presents a general framework for time series clustering based on spectral decomposition of the affinity matrix. We use the Gaussian function to construct the affinity matrix and develop a gradient based method for self-tuning the variance of the Gaussian function. The feasibility of our method is guaranteed by the theoretical inference in this paper. And our approach can be used to cluster both constant and variable length time series. Further our analysis shows that the cluster number is governed by the eigenstructure of the normalized affinity matrix. Thus our algorithm is able to discover the optimal number of clusters automatically. Finally experimental results are presented to show the effectiveness of our method.