Summary: We propose a new approximation technique for Hybrid Automata. Given any Hybrid Automaton $H$, we call Approx$(H$, $k)$ the Polynomial Hybrid Automaton obtained by approximating each formula $ϕ$ in $H$ with the formulae $ϕ_{k}$ obtained by replacing the functions in $ϕ$ with their Taylor polynomial of degree $k$. We prove that Approx$(H$, $k)$ is an over-approximation of $H$. We study the conditions ensuring that, given any $ε> 0$, some $k_{0}$ exists such that, for all $k > k_{0}$, the “distance” between any vector satisfying $ϕ_{k}$ and at least one vector satisfying $ϕ$ is less than $ε$. We study also conditions ensuring that, given any $ε> 0$, some $k_{0}$ exists such that, for all $k > k_{0}$, the “distance” between any configuration reached by Approx$(H$, $k)$ in $n$ steps and at least one configuration reached by $H$ in $n$ steps is less than $ε$.