The present invention is an improvement in a normally off-type high electron mobility transistor (HEMT) having a first single crystalline semiconductor layer, such as an undoped GaAs layer, and a second single crystalline semiconductor layer, such as an N-doped AlGaAs layer, having an electron affinity different from that of the first single crystalline semiconductor layer. A heterojunction is formed between the first and second single crystalline semiconductor layers. An electron-storing layer is formed adjacent to the heterojunctions serving as a conduction channel having a quasi two-dimensional electron gas. The concentration of electron gas is controlled by a gate electrode. An additional semiconductor layer, such as an N-doped GaAs layer, is formed at a portion of the second single crystalline layer in the area adjacent to the gate electrode. The additional semiconductor layer can generate the quasi two-dimensional electron gas even when no such gas is generated under the crystal parameter of the first and second single crystalline semiconductor layers. This generation of the quasi two-dimensional electron gas ensures that the HEMT has good reproducibility in respect to normally off-type operation.