Abstract Previous machine learning (ML) weather prediction models primarily focus on global mesoscale forecasting. This study develops three‐dimensional Fourier neural operator (FNO) models for simulating the dry convective boundary layer (CBL) at 800‐m grid spacing, which is a resolution in the gray zone. The filtered large‐eddy simulation data of the CBL are used for training the FNO models. The FNO models outperform traditional gray‐zone simulations in predicting a variety of flow statistics and instantaneous structures, including the scale of updrafts and downdrafts, the vertical profiles of statistics, and the energy spectra. The FNO models, trained using data for a few surface heat fluxes Qs=0.14−0.26Kms−1 ${Q}{s}=0.14-0.26,mathrm{K},mathrm{m},{mathrm{s} }^{-1}$, demonstrate certain generalization capability for other Qs ${Q}{s}$ within and out of this range Qs=0.1−0.3Kms−1 $left({Q}_{s}=0.1-0.3,mathrm{K},mathrm{m},{mathrm{s} }^{-1}right)$. The FNO model is a promising ML method for fast and accurate weather prediction in the gray zone.