We derive a fully non-linear optimal income tax schedule in the presence of private insurance. We fill the gap in the literature by studying the optimal tax formula with a comprehensive structure of the private markets—including incomplete markets models—both theoretically and quantitatively. As in the standard taxation literature without private insurance, the optimal tax formula can still be expressed in terms of standard sufficient statistics. With private insurance, however, the formula involves additional terms that reflect how the private market interacts with public insurance. For example, the optimal tax formula should also consider asset distribution and pecuniary externalities as well as the welfare effects of borrowing constraints.