In order to study the influence rule of the cutting parameters on the surface quality of aerospace aluminum alloy under the condition of absolute dry cutting and select reasonable cutting parameters, the turning test of 7075-T6 aluminum alloy was carried out by using the orthogonal test method, and the multivariate nonlinear regression model of the surface roughness and surface residual stress related to cutting elements was obtained. On this basis, the surface removal rate, surface residual stress and surface roughness were taken as the optimization targets, and the cutting three elements were taken as the optimization objects, the multiobjective optimization was carried out based on genetic algorithm, and the Pareto frontier was drawn. The optimal process parameters were selected from the optimal solution according to the actual processing demand. The results show that the surface roughness and surface residual stress are inversely proportional to the surface removal rate; the feed and the cutting speed are the main parameters affecting the surface roughness and surface residual stress; the increase of cutting depth can result in greater surface residual tensile stress only under minimum feed state.