Tungsten-chromium alloy (W-Cr alloy) is a primary candidate for plasma-facing materials (PFM) in future fusion devices because of its excellent properties. The knowledge of the interaction between solute Cr atoms and vacancy in W-Cr alloys is the key to understand the mechanism of the evolution of radiation damage. In this work the occupation of solute Cr atoms, the interaction between solute Cr atoms and vacancy, and the effect of the solute Cr concentration were studied by first-principles calculation. We found that the solute Cr atoms prefers to occupy the substitutional position with formation energy of ~0.3eV. The point defects induced by radiation will facilitate the segregation of the solute Cr atoms. The formation energy of solute Cr increases linearly with increasing of the concentration of solute Cr, indicating a strong segregation. It was also found that there exists a very weak attractive interaction between the solute Cr atoms and vacancy, and the interaction tends to be stronger when the concentration of the solute Cr increases. These results are important for understanding the long-term micro-structural evolution of materials under irradiation.