We describe a coupled climate model of intermediate complexity designed for use in global warming experiments. The atmospheric component is a two-dimensional (zonally averaged) statistical-dynamical model based on the Goddard Institute for Space Study's atmospheric general circulation model (GCM). In contrast with energy-balance models used in some climate models of intermediate complexity, this model includes full representation of the hydrological and momentum cycles. It also has parameterizations of the main physical processes, including a sophisticated radiation code. The ocean component is a coarse resolution ocean GCM with simplified global geometry based on the Geophysical Fluid Dynamics Laboratory modular ocean model. Because of the simplified geometry the resolution in the western boundary layers can be readily increased compared to conventional coarse resolution models, without increasing the model's computational requirements in a significant way. The ocean model's efficiency is also greatly increased by using a moderate degree of asynchronous coupling between the oceanic momentum and tracer fields. We demonstrate that this still allows an accurate simulation of transient behavior, including the seasonal cycle. A 100 years simulation with the model requires less than 8 hours on a state-of the art workstation. The main novelty of the model is therefore a combination of computational efficiency, statistical-dynamical atmosphere and 3D ocean. Long-term present-day climate simulations are carried out using the coupled model with and without flux adjustments, and with either the Gent-McWilliams (GM) parametrization scheme or horizontal diffusion (HD) in the ocean. Deep ocean temperatures systematically decrease in the runs without flux adjustment. We demonstrate that the mismatch between heat transports in the uncoupled states of two models is the main cause for the systematic drift. In addition, changes in the circulation and sea-ice formation also contribute to the drift. Flux adjustments in the freshwater fluxes are shown to have a stabilizing effect on the thermohaline circulation in the model, whereas the adjustments in the heat fluxes tend to weaken the global "conveyor". To evaluate the model's response to transient external forcing global warming simulations are also carried out with the flux-adjusted version of the coupled model. The coupled model reproduces reasonably well the behavior of more sophisticated coupled GCMs for both current climate and for the global warming scenarios.