Infrared spectra of the weakly bound van der Waals complex CH4-paraH(2) have been observed and analyzed for the first time. Measurements were made using a long-path (160-180 m) low-temperature (61-92 K) absorption cell which was probed with a Fourier transform spectrometer and a tunable diode laser. The partly resolved spectrum accompanying the S-0(0) pure rotational transition of H-2 around 350 cm(-1) was analyzed in terms of an approximate model to obtain the rotational and centrifugal distortion constants of the complex in its ground state. The high resolution spectrum accompanying the R(0) transition of the nu(4) fundamental band of CH4 near 1311 cm(-1) was assigned in detail and analyzed using the Coriolis model used previously for analogous spectra of methane-rare gas complexes. The effective intermolecular separation and dissociation energy of the complex in its ground state were determined to be about 4.12 Angstrom and 28 cm(-1), respectively.