The linear and non-linear optical properties of BiAlO3 are studied by employing the density functional perturbation theory within the local density and generalized gradient approximations. The computations are based on the electronic structure obtained within density functional theory. The optical properties such as the dielectric function, refractive index, spectral reflectivity, absorption coefficient and electron energy-loss spectrum are obtained in the energy region of up to 30 eV. The calculated value of the birefringence for BiAlO3 shows that it is a uniaxial negative crystal and has a large birefringence. We also report our studies on the second harmonic generation response coefficient over a large frequency range for BiAlO3 crystal. The predicted second-order optical spectra indicate pronounced structures related to of 1 and 2 frequency resonances. Furthermore, the non-linear optic and linear electro-optic coefficients are computed by employing 2n+1 theorem applied to an electric-field dependent energy functional. The results are compared with the available calculations.