The rovibrational energy levels and intensities of the CH3F–H2 dimer have been obtained using our recent global intermolecular potential energy surface [X.-L. Zhang et al., J. Chem. Phys. 148, 124302 (2018)]. The Hamiltonian, basis set, and matrix elements are derived and given for a symmetric top-linear molecule complex. This approach to the generation of energy levels and wavefunctions can readily be utilized for studying the rovibrational spectra of other van der Waals complexes composed of a symmetric top molecule and a linear molecule, and may readily be extended to other complexes of nonlinear molecules and linear molecules. To confirm our method, the rovibrational levels of the H2O–H2 dimer have been computed and shown to be in good agreement with experiment and with previous theoretical results. The rovibrational Schrödinger equation has been solved using a Lanczos algorithm together with an uncoupled product basis set. As expected, dimers containing ortho-H2 are more strongly bound than dimers containing para-H2. Energies and wavefunctions of the discrete rovibrational levels of CH3F–paraH2 complexes obtained from the direct vibrationally averaged 5-dimensional potentials are in good agreement with the results of the reduced 3-dimensional adiabatic-hindered-rotor (AHR) approximation. Accurate calculations of the transition line strengths for the orthoCH3F–paraH2 complex are also carried out, and are consistent with results obtained using the AHR approximation. The microwave spectrum associated with the orthoCH3F–orthoH2 dimer has been predicted for the first time.