A new mechanism (DeltaC1-DeltaC3 coupling) is accounted for the spin splitting of wurtzite GaN, which is originated from the intrinsic wurtzite effects (band folding and structure inversion asymmetry). The band-folding effect generates two conduction bands (DeltaC1 and DeltaC3), in which p-wave probability has tremendous change when kz approaches anti-crossing zone. The spin-splitting energy induced by the DeltaC1-DeltaC3 coupling and wurtzite structure inversion asymmetry is much larger than that evaluated by traditional Rashba or Dresselhaus effects. When we apply the coupling to GaN/AlN quantum wells, we find that the spin-splitting energy is sensitively controllable by an electric field. Based on the mechanism, we proposed a p-wave-enhanced spin-polarized field effect transistor, made of InxGa1-xN/InyAl1-yN, for spintronics application.