We have shown theoretically that the electron mobility in wurtzite AlN/GaN/AlN heterostructures can be enhanced by compensating the built-in electric field with the externally applied perpendicular electric field and by introducing a shallow In_xGa_1-xN channel in the center of GaN potential well. It was found that two- to fivefold increase of the room temperature electron mobility can be achieved. The tuning of the electron mobility with the external electric field or In_xGa_1-xN channel can be useful for the design of GaN-based field-effect transistors and optoelectronic devices.