This paper addresses a problem of recognizing human actions in video sequences. Recent studies have shown that methods which use bag-of-features and space-time features achieve high recognition accuracy. Such methods extract both appearance-based and motion-based features. This paper focuses only on appearance features. We proposeto model relationships between different pixel-level appearance features such as intensity and gradient using Brownian covariance, which is a natural extension of classical covariance measure. While classical covariance can model only linear relationships, Brownian covariance models all kinds of possible relationships. We propose a method to compute Brownian covariance on space-time volume of a video sequence. We show that proposed Video Brownian Covariance (VBC) descriptor carries complementary information to the Histogram of Oriented Gradients (HOG) descriptor. The fusion of these two descriptors gives a significant improvement in performance on three challenging action recognition datasets.