A new dynamical low-rank approximation based on time-dependent bases is developed for reduced-order modeling (ROM) of the scalar filtered density function (FDF). We formulate the stochastic Langevin equation as a matrix differential equation (MDE) and we approximate the MDE with a time-dependent low-rank matrix. We derive closed-form evolution equations for the approximate left and right singular vectors of the solution matrix. As a result, both row and column subspaces evolve with time. The presented low-rank approximation is not data-driven and the time-dependent subspace adapts to the dynamics of the flow on the fly. The resulting model is employed in LES-FDF of a non-premixed CO/H\_2 flame in a temporally evolving jet. For combustion chemistry, the syngas model involving 11 species is used. The results are appraised via {\it a posteriori} comparisons against data generated via full-rank LES-FDF and DNS of the same flame. The model yields excellent predictions of various statistics of the filtered thermo-chemistry variables.