In this study we present a series of LES simulations employing the Super-Droplet Method (SDM) for representing aerosol, cloud and rain microphysics. SDM is a particle-based and probabilistic approach in which a Monte-Carlo type algorithm is used for solving the particle collisions and coalescence process. The model does not differentiate between aerosol particles, cloud droplets, drizzle or rain drops. Consequently, it covers representation of such cloud-microphysical processes as: CCN activation, drizzle formation by autoconversion, accretion of cloud droplets, self-collection of raindrops and precipitation including aerosol wet deposition. Among the salient features of the SDM, there are: (i) the robustness of the model formulation (i.e. employment of basic principles rather than parametrisations) and (ii) the ease of comparison of the model results with experimental data obtained with particle-counting instruments. The model set-up used in the study is based on observations from the Rain In Cumulus over Ocean (RICO) field project (the GEWEX Cloud System Study Boundary Layer Cloud Working Group RICO case). Cloud and rain droplet size spectrum features obtained in the simulations are compared with previously published aircraft observations carried out during the RICO field project. The analysis covers height-resolved statistics of simulated cloud microphysical parameters such as droplet number concentration, effective radius, and the width of the cloud droplet size spectrum. The sensitivity of the results to the grid resolution of the LES, as well as to the sampling density of the probabilistic (Monte-Carlo type) model is discussed.