This paper introduces a multi-objective optimization framework for engineering design based on Kriging surrogate model when gradient information is available. Specifically, our interest here is to solve airfoil optimization problem via the use of computational fluid dynamics method. Here, the gradient is obtained via the adjoint method that computes the gradient for an arbitrary number of variables with a cost equal to or even less than one function evaluation. We applied the expected hypervolume improvement technique to add more solutions toward the discovery of Pareto front. The use of gradient-enhanced Kriging and expected hypervolume improvement eliminates the need for manual tuning of the weight as in the case of previous works regarding multi-objective airfoil optimization. The framework is demonstrated on the inviscid transonic airfoil optimization case with 2 and 12 design variables. The results show that the framework is highly efficient, outperforming non-gradient-based method in terms of optimization iteration. However, one has to be more careful when the actual gradient evaluation cost is counted. In our applications, the combination of gradient-enhanced Kriging and expected hypervolume improvement shows an advantage over the one with ordinary Kriging when the adjoint cost for two objectives is less than 20% of the function evaluation cost.