The main objective of the engineers and flight control system designers is to achieve the best performance and behavior of a controllable aeronautical vehicle. Trajectory optimization of a flying vehicle may improve performance, reduce costs, enhance the vehicle capabilities and lead to other favorable results. Trajectory Optimization is a knowledge that presents the ways of achieving optimum dynamic processes. Using the optimal control is one way to find the optimal trend of state variables. Since long range and endurance missions, require some forms of fuel management, there is ongoing research in the area of minimizing the fuel consumption. In current article, the problem of minimum fuel consumption for an unmanned aerial vehicle, during a circular maneuver in a predetermined area, is presented. UAV equations of motion are developed based on a point mass model. Optimality conditions of Pontryagen Minimum Principle (PMP) are found using the Hamiltonian function. Fuel consumption is the optimum performance index and multiple shooting method is chosen as numerical method for solving the problem at hand. Naturally, wind energy is expected to affect the flight path, so numerical simulations have been performed considering the effect of wind speed and direction on the optimal turn maneuver problem. Current research results show that in order to acquire a minimum fuel consumption loitering flight, in a circular trajectory, periodic climbing and descending maneuvers are needed.