In this paper we report the measurement of Lambda-doublet resolved state-to-state cross sections for inelastic collisions of OH by H-2 at a translational energy of 595 cm(-1). Experimental values are obtained for transitions from both the upper (f) and the lower (e) Lambda-doublet substates of the lowest rotational state (J = 3/2) of OH((2) Pi(3/2)) to almost all other states within the range of the collision energy. Cross sections for scattering by both para- and normal-H-2 have been determined. The main difference between para- and normal-H-2 scattering is seen in the Lambda-doublet cross section. The results are compared to He-scattering which shows that H-2 (J = 0) scattering behaves similar to He scattering. When averaged over the Lambda-doublet states, the cross sections are in good agreement with the measurements of Andresen et al. [J. Chem. Phys. 81, 571 (1984)], although the conclusions with regard to collisional pumping of interstellar OH masers are different. The quantum calculations of Offer et al. [J. Chem. Phys. 100, 362 (1994)] show a surprisingly good correspondence with the measured values. In this comparison the full initial state distribution of the OH and H-2 beams has been taken into account.