Icing on rotor blades can reduce aerodynamic characteristics and pose a serious threat to helicopter flight safety. The rotor undergoes periodic movement with variable pitch during forward flight, which can be simplified as the pitching oscillation process of the rotor airfoil. The unsteady characteristic of icing on oscillating airfoils presents a challenging problem compared to icing on fixed wings. To address this issue, numerical simulations of the unsteady airflow field in an unstructured overlapping grid system and the impact characteristics of supercooled water droplets based on the Euler method were conducted. Subsequently, the unsteady icing calculation method was improved based on Myers icing model. Additionally, a dynamic grid generation method called DGRBF (Radial Basis Function based on Delaunay Graph) was developed for multi-step icing calculations. A set of unsteady numerical simulation methods has been developed for icing on oscillating airfoils. The study analysed the effects of parameters such as average angle of attack, oscillation amplitude, and oscillation frequency on the icing process. In comparison to the static condition, the pitching motion of the airfoil takes into account the periodic variation of the angle of attack. The presence of a larger range of supercooled water droplets on the airfoil leads to increased icing and a higher icing limit. The final ice shape is not significantly affected by the oscillation frequency and amplitude of the airfoil's pitching motion at the average angle of attack. Additionally, there is no significant difference between the ice shape under the pitching motion and the ice shape at rest. Furthermore, the comparison between the numerical simulation results and the icing wind tunnel test results revealed a strong correlation in the macroscopic characteristics, including the icing limit, ice angle position, and maximum icing thickness. This confirms the accuracy and reliability of the calculation method. As a result, the developed unsteady icing numerical simulation method exhibits great potential for engineering applications.