In order to clarify formation kinetics of self-interstitial atoms (SIA) clusters in cubic silicon carbide (β-SiC) during irradiation, the nucleation and growth process of SIA-clusters have been investigated by a kinetic Monte-Carlo (KMC) simulation technique. It has been found from the KMC simulations that the formation kinetics of SIA-clusters in β-SiC during irradiation is classified into the following two types, depending on temperature. At relatively high temperatures, the thermal stability of an SIA-cluster is crucial for the nucleation and growth of the cluster, in which the composition of the cluster is almost stoichiometric. In contrast, at relatively low temperatures where the cluster thermal stability is no longer crucial, even an SIA-cluster far from stoichiometric composition is formed.