In this study, the aeroelastic instability of a wing with an initial out-of-plane curvature is determined. The structural dynamics of the wing is modelled by using the geometrically exact beam equations, and the aerodynamic loads are determined using an incompressible unsteady aerodynamic model. The wing is considered to have initial out-of-plane curvature, and the effect of the curvature on the flutter velocity and flutter frequency of the wing is determined. Two curved wing cases are considered here. In the first case, the length of the wing is assumed to be constant and therefore, as the wing is curved, the projected area of the wing decreases. In the second case, the wing is assumed to have a constant projected area and therefore different curvature angles result from different wing lengths. When the wing is designed to have an initial out-of-plane curvature, the wing dynamics change, and therefore the aeroelastic stability of the curved wing is also affected. It is shown that as the initial curvature of the wing increases, initially the flutter velocity decreases but then increases, and finally a sudden jump occurs in the flutter velocity due to the change of the coupled modes contributing to flutter. Moreover, the flutter frequency also first decreases as the curvature of the wing increases, and then there is a sudden jump in the frequency, and from this point again the frequency decreases. Finally, results highlighting the importance of the initial curvature and the length of the curved segment on the stability velocity and frequency of the curved wing are presented.