An efficient parallel Stokes’ solver has been developed for description of hydrodynamic interactions between Brownian particles in general geometries. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a hybrid Green’s function-finite element method. A scalable parallel computational framework is developed, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the general geometry Ewald-like method. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallel Stokes’ solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem leads to an efficient and parallel solver. We illustrate applications of the computational approach in the context of the dynamics of confined polymer and particles under equilibrium and non-equilibrium conditions. Acknowledgement: this work was supported by a grant from Chinese Academy of Sciences (No. 025GJHZ2022023MI).