We developed a new explicit cloud microphysical model, based on direct numerical simulation (DNS) with Lagrangian particle tracking. The model employs a vertically-elongated quasi-1D computational domain extending from the ground to the cloud top to explicitly capture the vertical structure of clouds. This allows us to simulate the all warm-cloud microphysical processes, including activation, condensation growth, collision-coalescence growth, and sedimentation. A homogeneous isotropic turbulence field is incorporated into this domain to explicitly resolve the turbulent wind fluctuations. Cloud microphysics simulations with and without turbulent wind fluctuations were performed to clarify the impact of turbulence on droplet growth. We obtained new insights into the altitude- and time-dependent microphysical statistics, which cannot be obtained through conventional DNS researches for a cubic box domain with periodic boundaries. The comparisons have shown that turbulence promoted the collision-coalescence growth of droplets. During the early developing stage, where the updraft was present, turbulence promoted the collisions between droplets with similar sizes (autoconversions) in the middle layer of the cloud. In later stage, relatively large droplets produced by autoconversions actively collected smaller droplets (accretions) in the middle and lower layers. The onset of precipitation at the ground occurred earlier and the first raindrop at the ground was larger in turbulence case than that in non-turbulence case.