A new three-dimensional (3D) magnetohydrodynamic (MHD) algorithm is described. The 3D MHD equations are solved in conservative form using a finite-volume scheme. The hydrodynamic variables in a cell are updated by calculating fluxes across the cell interfaces. The fluxes of mass, momentum and energy across cell interfaces are calculated by integrating a Boltzmann-like distribution function over velocity space. The novel feature of the method is that the distribution function incorporates most of the electromagnetic terms. In addition, the electric field along cell edges, which is used to update the magnetic field at cell faces, is also calculated using the Boltzmann-like distribution function. An important aspect of the method is that it provides a theoretical framework to incorporate additional terms in the 3D MHD equations (e.g. an anisotropic ion stress tensor and anisotropic temperature distributions).