Aiming at the online trajectory optimization for fixed-wing unmanned aerial vehicles (UAVs), this paper proposes a hp pseudospectral convex programming method based on differential operator model (hp PSCP-DOM). Firstly, the method utilizes the hp pseudospectral differential operator to obtain the change rate of control in the objective function, instead of the general extended dimension model (EDM). It can avoid introducing new variables and constraints, and makes the differential matrices sparse. Secondly, a lossless convexification method is used to transform the quadratic objective function into a linear objective function with a second-order conic (SOC) constraint. Thirdly, the dynamic and no-fly zone constraints are convexified through sequential linearization. The convex problem is then discretized using hp flipped Radau pseudospectral method (FRPM). It can achieve higher numerical accuracy with fewer discrete points. Finally, the problem is described as a sequential second-order conic programming (SSOCP) problem and solved by iterations. Simulation results show that even with a fixed large trust region radius, the proposed method can quickly converge to the optimal solution of the original problem. The analysis suggests that the method has potential for online trajectory optimization.