Antimicrobial peptides (AMPs) have attracted attention as next-generation antimicrobial drugs. Designing AMPs while considering multiple properties, such as antimicrobial activities and toxicity, requires numerous trials and errors by chemists. In this study, we propose MODAN, a machine learning-assisted AMP design framework based on multi-objective Bayesian optimisation. The primary advantage of MODAN is its ability to handle various non-proteinogenic amino acids, which have recently shown the potential of the activity enhancement, and this flexibility has not been achieved by previous works. In addition, multi-objective Bayesian optimisation enables simultaneous improvement of antimicrobial activity and toxicity. We have succeeded in designing peptides that have potent antimicrobial and low haemolytic activities within two rounds of MODAN recommendation and experimentation, based on a strategy that chemists do not usually consider.