Surrogate models are used as a substitute for sophisticated system analysis in engineering design in order to improve efficiency, enhance understanding of problem domains and facilitate multidisciplinary design trade-offs. However, the cost of acquiring knowledge and information needed to build high-quality surrogate models may greatly undermine the advantages of using them. This is particularly significant for building surrogate models in complex system design where collection of necessary modeling data can be extremely expensive. In the existing researches, though different Design of Experiment (DoE) techniques are proposed to reduce the cost of data collection, general guidelines are absent in applying these methods into different design scenarios in industrial practice. In our work, a study is conducted to investigate different DoE methods and their impact on building high-quality surrogate models for complex systems. Several DoE methods are studied and their effectiveness in highly nonlinear engineering domains are compared through case studies of a vehicle system design problem. This paper summarizes the study results and attempts to provide valuable knowledge for the related research and applications of DoE methods in building surrogate models for complex system designs.