A modified Oppenheimer-Brinkman-Kramers approximation (MOBK) is applied to calculate the K-shell capture cross sections in asymmetric collisions. In this MOBK formalism, a multielectron target atom is considered as a hydrogenic ion plus passive electrons. The correlation effect between the active and the passive electrons is expressed by a screening mean-field potential which is crucially important for the K-shell capture at intermediate impact energies. An analytical form is obtained for the total K-shell capture. For H⁺-nitrogen, oxygen, neon, and He²⁺-neon collisions, the calculated results show excellent agreement with the existing experimental findings in the intermediate energy interval. It is also shown that the present results well obey the scaling laws predicted by the OBK approximation.