Borrowing methodology from quantum mechanics, we propose and develop a density-matrix formalism for modal coupling and dispersion in mode-division multiplexing communications systems. The central concept in our formalism is the density matrix, from which all observable information of an optical field can be handily accessed. In the formalism, we derive fundamental evolution equations and concatenation rules for the key elements that characterize essential modal properties, and construct a statistical model ready for the numerical analysis of stochastic light propagation in randomly perturbed fibers. Unlike the Stokes-vector formalism that requires J2 - 1 auxiliary Gell-Mann matrices, the density-matrix formalism can be directly formulated for arbitrary modal-space dimension J. Based on the density-matrix formalism, the statistical modal properties of a 4-mode fiber under random perturbation are numerically investigated, which raises an interesting possibility of optimizing the modal dispersion by manipulation of the random perturbation.