The control of a wing-in-ground craft (WIG) usually allows for many needs, like cruising, speed, survival and stealth. Various degrees of emphasis on these requirements result in different trajectories, but there has not been a way of integrating and quantifying them yet. Moreover, most previous studies on other vehicles’ multi-objective trajectory is planned globally, lacking for local planning. For the multi-objective trajectory planning of WIGs, this paper proposes a multi-objective function in a polynomial form, in which each item represents an independent requirement and is adjusted by a linear or exponential weight. It uses the magnitude of weights to demonstrate how much attention is paid relatively to the corresponding demand. Trajectories of a virtual WIG model above the wave trough terrain are planned using reward shaping based on the introduced multi-objective function and deep reinforcement learning (DRL). Two conditions are considered globally and locally: a single scheme of weights is assigned to the whole environment, and two different schemes of weights are assigned to the two parts of the environment. Effectiveness of the multi-object reward function is analysed from the local and global perspectives. The reward function provides WIGs with a universal framework for adjusting the magnitude of weights, to meet different degrees of requirements on cruising, speed, stealth and survival, and helps WIGs guide an expected trajectory in engineering.