In this letter we investigate the throttling process of the charged Anti-de Sitter (AdS) black holes in the rainbow gravity. In the extended phase space of these black holes, the cosmological constant plays the role of a varying thermodynamic pressure and the black hole mass is identified with the thermodynamic enthalpy. We derive exact expressions for the Joule-Thomson coefficient and the inversion temperature in terms of black hole parameters and constants of rainbow gravity analytically, and then perform a numerical analysis for the isenthalpic and inversion curves of charged AdS black holes. Our calculations show all quantities are sensitive to rainbow parameter eta. We also discuss the isenthalpic curves for different values of the black hole mass. (C) 2019 The Author(s). Published by Elsevier B.V.