For multi-response quality improvement, this paper proposes a multi-response reliability-based robust design optimization (RBRDO) within an active learning multi-output Gaussian process (MGP) modeling framework. First, an active learning response surface modeling approach based on an improved D-optimal design is developed to enhance the utilization of experimental design points. Second, a covariance structure that captures correlations is specified to build the MGP, the expressions of its predictive partial derivatives are derived, and a risk cost function is formulated based on first-order second-moment theory. Then, a multivariate quality loss function is defined from the MGP outputs, upon which a parameter optimization model is established. Finally, a genetic algorithm is used to obtain the Pareto solution set, and the shortest distance method is applied to determine the optimal solution. Simulation results indicate that the proposed method effectively characterizes correlations among responses, improves the predictive accuracy of both the response surface and derivative prediction models, 〖JP3〗and yields optimal input parameter settings that balance robustness and reliability.