This paper presents a study of the leading-edge noise radiated by an airfoil undergoing a turbulent inflow. The noise prediction of generic airfoil profiles subjected to spanwise-varying inflow conditions is performed with the support of Amiet’s theory and the inverse strip technique. In the proposed methodology, the aeroacoustic transfer function of a generic airfoil profile is computed by the boundary element method. The effects of the airfoil leading-edge thickness on the inflow turbulence are accounted for by a turbulence spectrum based on the rapid distortion theory. This research shows that the turbulence distortion plays a significant role on the predicted noise levels. Compared with the von Kármán model for isotropic turbulence, the rapid distortion theory predicts reduced noise levels at high frequencies and increased noise levels at low frequencies. This paper also shows that the spanwise-varying inflow, here represented by a linearly changing condition, contributes to raising the noise levels when compared to the similar uniform inflow case. This research confirms that the finite airfoil thickness decreases the airfoil-gust lift response, consequently reducing the noise levels. This observation is more pronounced for microphones positioned downstream of the airfoil and for high frequencies.