In this paper, we have considered an anti-Kahler manifold (M, g, F) admitting a complex semi-symmetric non-metric F-connection $${\widetilde{\nabla }}$$ . First we study the properties of the curvature tensor, the conharmonic curvature tensor and the conformal curvature tensor of the connection $${\widetilde{\nabla }}$$ . Also, we investigate the condition for the anti-Kahler manifold (M, g, F) to be Einstein space with respect to the connection $${\widetilde{\nabla }}$$ . Finally, we define the dual connection of the connection $${\widetilde{\nabla }}$$ and present some results related to its curvature tensors.