  Let $X$ be a complex topological vector space with dim$(X)>1$ and
$\mathcal{B}(X)$ the space of all continuous linear operators on $X$. In this
paper, we extend the concept of supercyclicity of a single operators and
strongly continuous semigroups of operators to a subset of $\mathcal{B}(X)$. We
establish some results for supercyclic set of operators and we give some
applications for strongly continuous semigroups of operators and
$C$-regularized group of operators.
