This letter presents an optimal power flow model with the consideration of flexible transmission line impedance. By the use of big-M based complementary constraints, the original non-convex model can be transformed into a mixed integer quadratic programming that can be solved by branch and bound method. Numerical results from several test systems show that flexible transmission lines can provide better economic dispatch and reduce the total generation cost. Moreover, some infeasible optimal power flow scenarios can become solvable with optimal adjustment of the flexible transmission line impedance.