We propose a simple and elegant algorithm to track non-rigid objects using a covariance based object description and a Lie algebra based update mechanism. We represent an object window as the covariance matrix of features, therefore we manage to capture the spatial and statistical properties as well as their correlation within the same representation. The covariance matrix enables efficient fusion of different types of features and modalities, and its dimensionality is small. We incorporated a model update algorithm using the Lie group structure of the positive definite matrices. The update mechanism effectively adapts to the undergoing object deformations and appearance changes. The covariance tracking method does not make any assumption on the measurement noise and the motion of the tracked objects, and provides the global optimal solution. We show that it is capable of accurately detecting the non-rigid, moving objects in non-stationary camera sequences while achieving a promising detection rate of 97.4 percent.