Abstract This paper presents the numerical studies of the Magnus effect for a kinetic turbine of a horizontal axis. To focus on the Magnus blade, a single self-spinning cylindrical blade is assumed. An iterative direct- forcing immersed boundary method is employed within the Eulerian-Lagrangian framework due to its capability to treat complex and moving geometries. The Eulerian fluid domain is discretized using the finite volume method while the Magnus rotor is represented by a set of discrete points/markers. The aim of the numerical studies is to provide insights for the design process and predict aerodynamic performances under various operating conditions. Results for the self-spinning cylinder at laminar and turbulent flows are found to be in good agreement with published data. By decreasing the aspect ratio of the cylinder (simulated segment length over its diameter), an increase in lift coefficient and a decrease in drag coefficient was observed, which is believed to be attributed to a reduction in the three- dimensionality of the near-wake. For the Magnus rotor, key parameters, such as dynamic forcing and frequency, distribution of pressure coefficient and torque have been produced for two cases with different structural designs and working conditions. With increase of the aspect ratio, stable forces are observed from the root side of the blade and the torque coefficient is relatively larger, which indicates a superior performance in terms of power extraction.