Wing flutter analyses are carried out by a newly developed flow solution method using high-order flux reconstruction approach. The significance steps to be achieved are the moving boundary/moving grid technique in high-Reynolds number flows. The k-omega turbulence model is implemented for the objectives. The method is first validated by a forced oscillation and then fluid-structure coupled flutter simulations are carried out in subsonic flows. The predicted flutter boundary well agreed with previous numerical studies. It is found that 3rd- and 4th-order spatial accuracy produces almost the identical results in the presented cases, while the viscous effects the flutter boundary. Preliminary results in transonic flow with shock waves are also included. (C) 2015 The Authors. Published by Elsevier Ltd.