The characteristics of cold pools in the outer core of tropical cyclones under vertical wind shear of different magnitudes are investigated based on high-resolution idealized numerical simulations. The results suggest that the convective and non-convective cold pools in the outer core exhibit similar characteristics in different vertical wind shear magnitudes. Both two types of cold pools exhibit potential temperature, equivalent potential temperature, water vapor mixing ratio deficits and positive pressure perturbations. The depth of cold pools in the outer core of tropical cyclones is mostly less than 400 m, and the average strength is approximately 4~6 m/s, which is much smaller than that in mesoscale convective system. The depth is deeper and the intensity is also stronger significantly for non-convective cold pools, indicating that the intensity of different types of cold pool is not only related to the potential temperature perturbation, but also depends on its depth. The cold pools are caused by widespread convective-scale downdrafts, and the downward vertical mass transport in convective cold pools caused by stronger downdrafts is almost twice that of non-convective ones. Budgets of surface perturbation pressure induced by downdrafts indicate that subcloud evaporational cooling and water loading are conducive to high pressure near the surface in cold pools, while in-cloud warming due to latent heat release leads to a pressure decrease. Moreover, the greater effects of precipitation drag and subcloud evaporation in convective cold pools result in more significant pressure increasement than that in non-convective cold pools. The features of both types of cold pools also varies with the increase in the shear value. There are mostly micro-scale and discrete convective cold pools in the weak-shear environment. As shear increases, the total number of outer-core cold pools and the frequency of convective cold pools decreases while the non-convective ones with larger range and mostly linked to dissipated convection increases, deepen and intensify, in addition. There are weaker outflow but stronger cyclonic velocity caused by both two types of cold pools with the shear magnitude increased.