Surface adsorption of a solution is still a challenging problem in the thermodynamics of surfaces. In this work, a new thermodynamic state function is defined. The equilibrium condition of surface adsorption is that the differential of this state function is equal to zero. Based on this condition, we derived a new equation to describe surface adsorption at equilibrium. No hypothetical dividing surface is needed in this derivation. The new equation is quite different from the Gibbs adsorption equation. We also performed molecular dynamic simulations of aqueous sodium chloride solutions. The simulated results are in good agreement with our theoretical predictions.