Due to the strong nonlinearity and nonholonomic dynamics, despite the various general trajectory optimization methods presented, few of them can guarantee efficient computation and physical feasibility for relatively complicated fixed-wing UAV dynamics. Aiming at this issue, this paper investigates a differential flatness-based trajectory optimization method for fixed-wing UAVs (DFTO-FW). The customized trajectory representation is presented through differential flat characteristics analysis and polynomial parameterization, eliminating equality constraints to avoid the heavy computational burdens of solving complex dynamics. Through the design of integral performance costs and derivation of analytical gradients, the original trajectory optimization is transcribed into a lightweight, unconstrained, gradient-analytical optimization with linear time complexity to improve efficiency further. The simulation experiments illustrate the superior efficiency of the DFTO-FW, which takes sub-second CPU time (on a personal desktop) against other competitors by orders of magnitude to generate fixed-wing UAV trajectories in randomly generated obstacle environments.