We study theoretically linear and nonlinear change of refractive index as well the linear and nonlinear optical absorption in a cylindrical quantum dot (CQD) in the presence of a uniform magnetic field by using the formalism of matrix density and perturbation method. The energy levels and wave functions of an electron in the CQD were obtained by solving the Schrodinger equation independent of time within the effective mass approximation. Numerical calculations are performed for a CQD GaAs/GaAlAs. It was found that the position of the resonance peaks, shifts to regions of lower energies (red shift) when the magnetic field intensity decreases and the dimensions of the nanostructure increases.