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We present a multi-objective Bayesian active learning strategy, which greatly accelerates the discovery of super high-strength and high-ductility lead-free solder alloys. The active learning strategy demonstrates that a machine learning model will have high generalizability if experimental data uncertainty is included, which greatly improves the model prediction or the material design accuracy. The feature-point-start forward method in multi-objective optimization adopts two Gaussian process regression (GPR) models, one for strength and one for elongation, and their outputs build up the acquisition-function-modified objective space of strength and elongation. Then, Bayesian sampling is applied to design the next experiments by balancing exploitation and exploration. Seven multi-objective active learning iterations discovered two novel super high-strength and high-ductility lead-free solder alloys. After that, various material characterizations were conducted on the two novel solder alloys, and the results exhibited their high performances in melting properties, wettability, electrical conductivity, and shear strength of the solder joint and explored the mechanism of high strength and high ductility of the alloys. The present work systematically analyzes the important role of experimental uncertainty in machine learning, especially in the global optimization for material design, which demands high generalizability of predictions. [ABSTRACT FROM AUTHOR]