We introduce a composite kernel learning (CKL) technique to construct new kernel (covariance) functions for efficient surrogate modeling in engineering design. The CKL technique works by constructing a new kernel from the weighted sum combination of existing kernels where the weights and hyperparameters of Kriging are simultaneously trained. By deploying Kriging with CKL, we aim to better capture the input-output relationship of black-box functions in engineering design problems through the construction of more suitable kernels. The effectiveness of CKL-Kriging is demonstrated on two computational fluid dynamics-based problems, that is, an axial transonic rotor problem and a centrifugal diffuser design problem. The results show that the Kriging with CKL generally outperforms or performs similarly to the best performing kernel on the two test problems. In light of the results, we infer that Kriging with CKL is a promising surrogate modeling technique to be deployed for general engineering design problems.