We have measured pressure broadening and line shift parameters for the J=1 <-- 0 and J=2 <-- 1 transitions of carbon monoxide (CO) in collision with hydrogen (H-2) at various temperatures between 8 and 600 K. Because of the abundance of both species in the interstellar medium, the CO-H-2 collision system is of astrophysical importance. Measurements below 35 K were made using the collisional cooling technique, while measurements at higher temperatures were made in a conventional equilibrium cell. These measurements were compared with theoretical results of quantum scattering calculations using the currently best available potential surface for the CO-H-2 collision system. We find a good agreement between theory and experiment at higher temperatures (> 30 K) while for lower temperatures considerable deviations occur. (C) 2000 American Institute of Physics. [S0021-9606(00)01108-9].