The present thesis deals with the issue of condensational growth of cloud droplets, with a special emphasis on probing the evolution of their size spectrum. A simplified model of an ascending cloud parcel was introduced. This model includes turbulence as well as microphysical variability. Basing on the assumed model, a numerical simulation of the evolution of a cloud parcel was created in C++. The obtained results differ significantly from the results of simulations based on simpler models, those not including local microphysical variability in a cloud parcel. They (the results) are, first and foremost, the broadening of the cloud droplet radius spectrum in the case of the average vertical velocity <w> in the range of 1 - 3 m/s, as well as the change of droplet activation rate in the case of <w> equalling 0,5 m/s and 1 m/s.