The numerical modeling of two-phase flows in complex geometries is of special relevance in many scientific and industrial applications. In this paper, we describe a numerical method to perform three-dimensional simulations of such flow problems. This method adopts a volume-of-fluid (VOF) approach to capture and advance the fluid interface, and it integrates the fluid solver with the immersed boundary (IB) modeling of arbitrary-shape walls and moving bodies. The shape and movement of solid geometries are efficiently represented by an auxiliary signed distance function (SDF) with local coordinate transformation. Validation tests have been conducted using the present method, and the computational results are in good agreements with reference solutions and experimental data. We further present its application to the simulation of the air-water flow in a twin screw kneader. Hence, the adequacy and suitability of the present VOF-IB method are shown to successfully simulate complicated two-phase flows interacting with general geometries. (C) 2015 Elsevier Ltd. All rights reserved.