A precipitating convective cloud is simulated successfully using the Lagrangian cloud model, in which the flow field is simulated by large eddy simulation and the droplets are treated as Lagrangian particles, and the results are analyzed to investigate precipitation initiation and to examine the parameterization of cloud microphysics. It is found that raindrops appear initially near the cloud top, in which strong turbulence and broadened droplet spectrum are induced by the entrainment of dry air, but high liquid-water mixing ratio is maintained within cloud parts because of insufficient mixing. Statistical analysis of the downward vertical velocity of a droplet W reveals that the transition from cloud droplets to raindrops occurs in the range 20 mu m < r < 100 mu m, while the variation of W depends on turbulence as well as the droplet radius r. The general pattern of the raindrop size distribution is found to be consistent with the Marshall-Palmer distribution. The precipitation flux can be underestimated substantially, if the terminal velocity is used instead of W, but it is not sensitive to the choice of the critical droplet radius dividing cloud drops and raindrops. It is also found that precipitation starts earlier and becomes stronger if the effect of turbulence is included in the collection kernel.