The recently synthesized air-insensitive hydrogen doped KCr 3 As 3 superconductor has aroused great research interests. This material has, for the first time in the research area of the quasi-one-dimensional Cr-based superconductivity (SC), realized a tunability through charge doping, which will potentially significantly push the development of this area. Here based on the band structure from first-principle calculations, we construct a sixband tight-binding (TB) model equipped with multi-orbital Hubbard interactions, and adopt the random-phaseapproximation approach to study the hydrogen-doping dependence of the pairing symmetry and superconducting T c . Under the rigid-band approximation, our pairing phase diagram is occupied by the triplet p z -wave pairing through out the hydrogen-doping regime x ∈ (0.4, 1) in which SC has been experimentally detected. Remarkably, the x-dependence of T c shows a peak at the 3D-quasi-1D Lifshitz transition point, although the total density of state exhibit a dip there. A thorough investigation of the band structure reveals type-II van-Hove singularities (VHSs) in the γ band, which favor the formation of the triplet SC. It turns out that the γ-Fermi surface (FS) comprises two flat quasi-1D FS sheets almost parallel to the k z = 0 plane and six almost perpendicular tube-like FS sheets, and the type-II VHS just lies in the boundary between these two FS parts. Furthermore, the |k z | of the VH planes reaches the maximum near the Lifshitz-transition point, which pushes the T c of the p z -wave SC to the maximum. Our results appeal more experimental access into this intriguing superconductor.