Based on the deficiency of fixed-kernel in the traditional time–frequency distribution, which is lack of adaptability, a new adaptive kernel function, which is named as the adaptive radial sinc kernel, is proposed according to design criteria of adaptive optimal kernel. The definition and algorithm of radial sinc kernel are given, and the proposed method is compared with the tradition time–frequency distribution. The simulation results show that the proposed method is superior to the traditional fixed-kernel functions, such as Wigner–Ville distribution, Choi–Williams distribution, cone-kernel distribution and continuous wavelet transform. The adaptive radial sinc kernel can overcome the deficiency of fixed-kernel function in traditional time–frequency distribution, adopt the optimizing method to filter the cross-terms adaptively according to the signal distribution, obtain good time–frequency resolution and has extensive adaptability for an arbitrary signal. Finally, the proposed method has been applied to the fault diagnosis of rolling bearing, and the experiment result shows that the proposed method is very effective.