Multiobjective optimization problems (MOPs) are prevalent in machine learning, with applications in multi-task learning, learning under fairness or robustness constraints, etc. Instead of reducing multiple objective functions into a scalar objective, MOPs aim to optimize for the so-called Pareto optimality or Pareto set learning, which involves optimizing more than one objective function simultaneously, over models with millions of parameters. Existing benchmark libraries for MOPs mainly focus on evolutionary algorithms, most of which are zeroth-order methods that do not utilize higher-order information from multiple objectives and cannot scale to large-scale models with millions of parameters. In light of the above gap, this paper introduces \algoname, the first multiobjective optimization library that supports state-of-the-art gradient-based methods, provides a fair benchmark, and is open-sourced for the community.\footnote{\algoname~is available at \url{https://github.com/xzhang2523/libmoon} and can be installed via ``\texttt{pip install libmoon}''.