In this paper, we propose a high-order finite volume hybrid kinetic Weighted Essentially Non-Oscillatory (WENO) scheme for inviscid and viscous flows. Based on the WENO reconstruction technique, a hybrid kinetic numerical flux is introduced for the present method, which includes the mechanisms of both the free transfer and the collision of gas molecules. The collisionless free transfer part of the hybrid numerical flux is constructed from the conventional kinetic flux vector splitting treatment, and the collision contribution is considered by constructing an equilibrium gas state and calculating the corresponding numerical flux at the cell interface. The total variation diminishing Runge-Kutta methods are used for the temporal integration. The high-order accuracy and good shock-capturing capability of the proposed hybrid kinetic WENO scheme are validated by many numerical examples in one-dimensional and two-dimensional cases. Copyright (C) 2015 John Wiley & Sons, Ltd.