Multi-view feature learning is an attractive research topic with great practical success. Canonical correlation analysis (CCA) has become an important technique in multi-view learning, since it can fully utilize the inter-view correlation. In this paper, we mainly study the CCA based multi-view supervised feature learning technique where the labels of training samples are known. Several supervised CCA based multi-view methods have been presented, which focus on investigating the supervised correlation across different views. However, they take no account of the intra-view correlation between samples. Researchers have also introduced the discriminant analysis technique into multi-view feature learning, such as multi-view discriminant analysis (MvDA). But they ignore the canonical correlation within each view and between all views. In this paper, we propose a novel multi-view feature learning approach based on intra-view and inter-view supervised correlation analysis (I2SCA), which can explore the useful correlation information of samples within each view and between all views. The objective function of I2SCA is designed to simultaneously extract the discriminatingly correlated features from both inter-view and intra-view. It can obtain an analytical solution without iterative calculation. And we provide a kernelized extension of I2SCA to tackle the linearly inseparable problem in the original feature space. Four widely-used datasets are employed as test data. Experimental results demonstrate that our proposed approaches outperform several representative multi-view supervised feature learning methods.