Fixed-wing unmanned aerial vehicle formations have been widely used in various civil and military fields, where the trajectory planning is a key issue that determines the mission execution performance. Existence of highly nonlinear constraints makes the feasible solution space extremely non-convex and hard to search. Hence, currently methods generally rely heavily on high-quality initial guesses, and are susceptible to the obstacle distribution. In this paper, an optimal control-based method with warm-start is proposed to overcome these limitations. First, the trajectory planning is formulated as an optimal control problem by analyzing necessary constraints. Secondly, aiming at high-quality homotopic warm-start, an improved artificial potential field method that caters to eliminating local oscillation, inter-formation coordination and satisfaction on physical constraints is designed. Last but not the least, a loosen formation constraint strategy is integrated to expand the solution space, thus facilitating the convergent process. Numerical simulations under different complexities show the proposed planner is efficient and robust, where the designed warm-start strategy contributes much to the convergence. Meanwhile, the proposed planner exhibits promising performance to solve the problem for multiple formations.