With　the　development　of　automatic　driving　technology　and　the　internet　of　vehicles,　platooning　based　on　control　of　connected　autonomous　vehicles　has　become　one　of　the　most　promising　approaches　to　improve　traffic　efficiency.　This　paper　studies　the　control　problem　of　mixed　vehicle　platoons　consisting　of　human-driven　vehicles　and　connected　autonomous　vehicles.　Firstly,　we　propose　a　data-driven　method　to　model　mixed　vehicle　platoons　based　on　Koopman　operator　theory.　This　method　gives　a　way　to　represent　the　mixed　vehicle　platoon　by　a　linear　model　in　a　high-dimensional　space,　the　approximation　of　which　is　obtained　by　a　neural　network　framework.　Secondly,　we　employ　model　predictive　control　(MPC)　to　address　the　platoon　control　problem　of　mixed　vehicle　platoons,　where　both　centralized　MPC　and　distributed　MPC　algorithms　are　designed.　Finally,　the　effectiveness　of　the　data-driven　modeling　method　and　the　centralized/distributed　MPC　algorithms　is　verified　by　numerical　simulations.　It　is　revealed　that　the　proposed　data-driven　DMPC　algorithm　exhibits　comparable　control　performance　with　less　computation　cost　compared　with　the　centralized　MPC　algorithm,　and　it　shows　faster　convergence　speed　than　the　nonlinear　model　based　DMPC　algorithm.