As is well known, the structure inversion asymmetry (SIA) and Rashba spin splitting of semiconductor heterostructure can be modulated by either electric field or engineering asymmetric heterostructure. In this paper, we calculate the Rashba coefficient and Rashba spin splitting for the first subband of Al0.6Ga0.4N/GaN/Al0.3Ga0.7N/Al0.6Ga0.4N QW each as a function of thickness (ws) of the inserted Al0.3Ga0.7N layer (right well) and external electric field. The thickness of GaN layer (left well) is 40-ws . With ws increasing, the Rashba coefficient and Rashba spin splitting for the first subband increase first, because the polarized electric field in the well region increases and the electrons shift towards the left heterointerfaces, and then decrease when ws20 since the electric field in the well region decreases, and the confined energy increases as effective well thickness decreases. But when ws30 , the Rashba spin splitting decreases more rapidly, since kF decreases rapidly. Contributions to the Rashba coefficient from the well is largest, lesser is the contribution from the interface, which varies slowly with ws, and the contribution from the barrier is relatively small. Then we assume ws=20 , and find that the external electric field can modulate the Rashba coefficient and Rashba spin splitting greatly because the contribution to the Rashba coefficient from the well changes rapidly with the external electric field, and the external electric field brings about additional potential and affects the spatial distribution of electrons, confined energy and Fermi level. When the direction of the external electric field is the same as (contrary to) the polarization electric field, the Rashba coefficient and Rashba spin splitting increase (decrease) with external electric field increasing. With the external electric field changing from -1.5108 V m-1 to 1.5108 V m-1, the Rashba coefficient approximately varies linearly, and the Rashba spin splitting first increases rapidly, then approximately increases linearly, and finally increases slowly. Because the value of kF increases rapidly first, then increases slowly. Results show that the Rashba coefficient and the Rashba spin splitting in the Al0.6Ga0.4N/GaN/Al0.3Ga0.7N/Al0.6Ga0.4N QW can be modulated by changing the relative thickness of GaN and Al0.3Ga0.7N layers and the external electric field, thereby giving guidance for designing the spintronic devices.