QSW MPI is a python package developed for the modeling of quantum stochastic walks, a generalization of the classical random walk and continuous-time quantum walk in the Lindblad formalism. This model allows for the study of a wide range of Markovian open quantum systems subject to varying degrees of incoherent scattering. Consisting of a python interface built on parallelized Fortran libraries utilizing sparse data structures; QSW MPI is scalable to massively parallel computers, making possible the simulation of walks on graphs with many thousands of vertices. QSW MPI also provides explicit support for an extension of the standard quantum stochastic walk model to the study of non-Hermitian absorption and emission processes.