To study the burnup features of accelerator-driven subcritical systems (ADSs), simplified transmutation trajectories are imperative to make the simulation process more effective with acceptable precision. This process has long been considered a challenging task since the construction of simplified burnup chains often need complex judgments and experiences. Additionally, the burnup analysis of ADSs requires more specific burnup chains for some important isotopes with minor actinides (MAs) and long-lived fission products (LLFPs) included. However, some general burnup codes lack these chains or pack some particularly important isotopes into a kind of pseudo nuclide. In this context, a PyNE-based burnup module (PyNE-Burn) has been developed to solve the burnup problem in ADSs, where three types of isotopes have been considered to construct the simplified burnup chains and weight-sorted judgment criteria have been proposed to determine which nuclides should be included. Moreover, the scan-mode-method-based high-order differential expression has been employed to substitute the legacy method in solving the linearized burnup chains. Finally, numerical tests have been carried out to demonstrate that the PyNE-Burn module has acceptable accuracy and can be used in dealing with the burnup problem in ADSs.