A new adaptive mesh refinement wave-packet tracking approach is presented that can be used for efficient transition prediction of hypersonic boundary layer flows. In the current study we focus on convectively linearly unstable boundary layer flows although this method is not limited to convective instabilities. The wave-packet tracking strategy uses a higher- order accurate adaptive mesh refinement strategy that provides significant computational savings over conventional static mesh approaches. This method can also be employed for highly complex geometries. The efficiency and accuracy of the current approach strongly depends on the implementation details, refinement criteria and the flow quantities that are used for tracking. A detailed description of this method and the computational expense will be discussed and compared to other more conventional approaches.