In this talk, we first introduce the bi-fidelity stochastic collocation method in uncertainty quantification, then adopt it to solve a class of kinetic models with random parameters and multiple scalings. We use the Boltzmann and linear transport models as examples to illustrate our idea, with different strategies of choosing the low-fidelity models in our bi-fidelity approximation. A formal uniform-in-Knudsen number error estimate, practical error bound and numerical experiments will be presented to demonstrate the accuracy and efficiency of the proposed method. This is a joint work with Xueyu Zhu and Lorenzo Pareschi.