Self-compression of an ultrashort pulse in a hollow-core waveguide filled with noble gas is a simple and promising approach to generate few and even single-cycle pulses. However, when the input pulse energy approaches to mJ level, ionization of the gas induces strong higher-order dispersion through multiple mechanisms, which makes the temporal compression process unstable and even fail. In this paper, we systematically study the effects of higher-order dispersion in the self-compression process of mJ few-cycle pulses. We found that the self-compression depends on the approaching routine of group delay dispersion and third-order dispersion optimization. There exists a steady and stable routine to maintain the pulse duration around the Fourier transform limit. Then, we successfully demonstrate stable and repeatable compression of 3 mJ pulses to 13.1 and 10.5 fs in a 2 cm hollow-core waveguide filled with Ar and Kr, respectively.