Ice ridges can cause degradation of wing aerodynamic performance， which is an important factor endangering flight safety. The air flow field is obtained by solving the N-S equations using the structured mesh and the central finite volume method. The Lagrange method is used to obtain the impingement characteristics of the water droplets. The ice accretion of NACA 0012 airfoil is numerically simulated based on the Messinger icing thermodynamic model. The ice shapes are in good agreement with the experimental data， which verifies the accuracy and feasibility of the calculation method. Based on this， the anti-icing zone is set on the NACA 0012 airfoil and the anti-icing thermal load is considered. The formation of ice ridges under supercooled large droplet （SLD） conditions is simulated. The effects of ambient temperature， the liquid water content and the thermal load on the formation of ice ridges are investigated. Besides， the effects of nanosecond dielectric barrier discharge （NSDBD） plasma actuator on the formation of the ice ridges are numerically simulated by placing the NSDBD over the ridge locations under the SLD conditions. The results show that in the case of SLDs， the growth of ambient temperature results in the extent of ice ridges is increased and the height is decreased； the increase of liquid water content leads to the increase of both the extent and the height of ice ridges； improving the anti-icing thermal load can promote the evaporation within the anti-icing area， and then reduce the ice ridges formation； in the case of the SLDs， the droplets may impinge on the position outside the anti-icing area of the lower surface， which may result in the ice ridges； the heating effect of the NSDBD on the air promotes the evaporation， which may keep the ice ridges from forming at the small liquid water content level and push back the formation position of ice ridges under the high liquid water content.