Graphene is highly flexible and widely used in flexible devices. However, is the oxidized graphene more flexible than graphene? This is still under debate between simulations and experiments. By employing density functional theory calculations, we show that the bending modulus of oxidized graphene is quite tunable by changing the type and coverage of the functional groups, as well as the bending direction. The hydroxyl increases the bending modulus of graphene, but epoxide can degrade the bending modulus in the armchair bending direction, making the oxidized graphene more flexible than graphene. On the other hand, there exists a curvature limit during bending the oxidized graphene, where OH hydrogen bonds start to transform into O-H covalent bonds. Generally, our results demonstrate the effects of the functional groups and bending direction on the flexibility of oxidized graphene, which should be helpful to design graphene-based flexible devices.