A semiconductor device according to an embodiment includes a first semiconductor layer of a first GaN based semiconductor, a second semiconductor layer of a second GaN based semiconductor having a band gap narrower than the first GaN based semiconductor, a third semiconductor layer of a third GaN based semiconductor having a band gap wider than the second GaN based semiconductor, a fourth semiconductor layer of a fourth GaN based semiconductor having a band gap narrower than the third GaN based semiconductor, a fifth semiconductor layer of a fifth GaN based semiconductor having a band gap wider than the fourth GaN based semiconductor, a gate dielectric provided directly on the third semiconductor layer, the fourth semiconductor layer, and the fifth semiconductor layer, a gate electrode provided on the gate dielectric, a source and drain electrodes provided above the fifth semiconductor layer.