The linear and nonlinear optical absorption coefficients (ACs) and refraction index changes (RICs) of 1s–1p, 1p–1d, and 1f–1d transitions are investigated in a wurtzite InxGa1 – xN/GaN core–shell quantum dot (CSQD) with donor impurity by using density matrix approach. The effects of built-in electric field (BEF), ternary mixed crystal (TMC), impurity, and CSQD size are studied in detail. The finite element method is used to calculate the ground and excited energy state energy and wave function. The results reveal that the BEF has a great influence on the linear, nonlinear, and total ACs and RICs. The presence of impurity leads the resonant peaks of the ACs and RICs to be blue-shifted for all transitions, especially for 1s–1p transition. It is also found that the resonant peaks of the ACs and RICs present a red shift with In-composition decreasing or core radius increasing. Moreover, the amplitudes of the ACs and RICs are strongly affected by the incident optical intensity. The absorption saturation is more sensitive without the impurity than with the impurity, and the appearance of absorption saturation requires a larger incident optical intensity when considering the BEF.