Stability of hydrogen (H) in tungsten (W) with carbon (C) impurity is investigated by using the first-principles method. In intrinsic W, C exhibits a week attractive interaction with H at a distance of ～2.5Å, and it is the most stable site of H in the bulk W with C. In the presence of the monovacancy in W, H prefers to bind onto an isosurface of the same charge density of 0.10 Å-3, due to the existence of C. Our research finds that the monovacancy in W can contain only ten H atoms and H molecule cannot be formed in comparison with the result without C, suggesting a strong effect of C on H stability in W. When two C atoms exit in the vacancy, the charge density of the isosurface that H binds onto is 0.13 Å-3.