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Streamwise acceleration of the background flow field is one of various effects occurring when wind turbines operate under non-idealized conditions, such as in complex terrain or in dense wind farms. Thus, studying this effect is essential to improve understanding of aerodynamic performance in these cases. In the present work, a simple model based on momentum theory is derived for the situation of an actuator disc (AD) operating in a background flow field with a constant velocity gradient. Reynolds-averaged Navier-Stokes (RANS) simulations of this scenario are performed, showing that a positive acceleration yields a reduction of induction and vice versa, a negative acceleration leads to an increase of induction. The new model accurately captures this behavior and reduces the prediction error by eighty percent compared to classical momentum theory where the effect of the background flow acceleration is disregarded. Further analysis suggests that the model can be extended to a formulation in which an even higher prediction accuracy can be achieved.