In this paper, the effect of incident light intensity, relaxation time, core radius and shell thickness on linear, nonlinear, total optical absorption coefficients and refractive index changes in GaN/Al0.1Ga0.9N core–shell nanowire are theoretically investigated. The presented nanostructure is a cylindrical quantum wire including a shell around the cylinder core. By numerical solution of Schrödinger equation in the cylindrical coordinates with effective mass approximation, the optical absorption coefficients are calculated. The results show that the magnitude of optical absorption coefficients can be adjusted by varying the relaxation time. The positions of resonant peaks of optical absorption coefficients are redshifted by increase of core radius due to decrease of the energy difference between two energy levels. With increase of shell thickness initially, the resonance wavelength of absorption coefficient increases (redshift) and magnitude of absorption coefficient decreases. Then with more increases of the shell thickness, redshifting of resonance wavelength is stopped and magnitude of absorption coefficient is increased. There is a significant increase in the refractive index change with increase of relaxation time.