We consider the problem of testing graph expansion (either vertex or edge) in the bounded degree model [Goldreich, Ron 2000]. We give a property tester that given a graph with degree bound $$d$$, an expansion bound $$\alpha$$, and a parameter $$\epsilon > 0$$, accepts the graph with high probability if its expansion is more than $$\alpha$$, and rejects it with high probability if it is $$\epsilon$$-far from any graph with expansion $$\alpha’$$ with degree bound $$d$$, where $$\alpha’ < \alpha$$ is a function of $$\alpha$$. For edge expansion, we obtain $$\alpha’ = \Omega(\frac{\alpha^2}{d})$$, and for vertex expansion, we obtain$$\alpha’ = \Omega(\frac{\alpha^2}{d^2})$$. In either case, the algorithm runs in time $$\tilde{O}(\frac{n^{(1+\mu)/2}d^2}{\epsilon\alpha^2})$$ for any given constant $$\mu > 0$$.