Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The degree of a vertex $a\in V(G)$ is denoted by $d_{G}(a)$. The general sum-connectivity index of $G$ is defined as $\chi_{\alpha}(G)=\sum_{ab\in E(G)}(d_{G}(a)+d_{G}(b))^{\alpha}$, where $\alpha$ is a real number. In this paper, we compute exact formulae for general sum-connectivity index of several graph operations. These operations include tensor product, union of graphs, splices and links of graphs and Hajós construction of graphs. Moreover, we also compute exact formulae for general sum-connectivity index of some graph operations for positive integral values of $\alpha$. These operations include cartesian product, strong product, composition, join, disjunction and symmetric difference of graphs.