Abstract Convection-permitting resolutions, which refer to kilometer-scale horizontal grid spacings, have become increasingly popular in regional numerical weather prediction and climate studies. However, this resolution range is in the gray zone for the simulation of convection, where conventional cumulus convection and subgrid-scale (SGS) turbulence parameterizations are inadequate for such grid spacings due to invalid assumptions and simplifications. Recent studies demonstrated that the magnitudes of SGS fluxes of momentum and scalars are comparable to those of resolved fluxes at convection-permitting resolutions and that horizontal SGS components are as important as the vertical SGS component. Thus, it appears necessary to adapt available schemes to model the SGS effects of convective motions for the gray zone. Here, we investigated the efficacy of separately parameterizing the vertical and horizontal SGS effects in improving the convection-permitting simulation of Typhoon Vicente (2012). To represent the vertical SGS turbulence effect, we evaluated the Grell-3, Tiedtke, and multiscale Kain–Fritsch (MSKF) schemes in the Weather Research and Forecasting (WRF) Model; the MSKF scheme is scale adaptive, whereas the other two are conventional cumulus schemes. For horizontal SGS turbulence, we evaluated the effects of the traditional Smagorinsky scheme and our newly developed reconstruction and nonlinear anisotropy (RNA) model, which models not only downgradient diffusion but also backscatter. We found that the simulation combining the MSKF and RNA schemes exhibits the best skill in predicting precipitation, especially rainfall extremes. The advantages are rooted in the MSKF scheme’s scale-awareness and parameterized cloud–radiation feedback and in the backscatter-enabling capability of the RNA model. Significance Statement Operational numerical weather prediction and some climate simulations have approached kilometer-scale horizontal resolutions, called convection-permitting resolutions. However, details of convective storms are not well represented at these resolutions, and small-scale fluid motions can potentially impact the overall simulation performance. In practice, the effects of such unresolved turbulent eddies were once neglected. We suggest representing these effects in the vertical and horizontal directions with an adaptive cumulus convection parameterization and an advanced turbulence model, respectively, which significantly improve the simulation of tropical cyclones. This framework allows us to adapt convection schemes developed by the mesoscale modeling community and turbulence schemes studied by large-eddy simulation groups for representing three-dimensional turbulence in the convection-permitting regime.