A nonlinear weathervaning control algorithm for offshore vessels is designed in the task space under consideration of Lyapunov stability theory. When a Dynamic Positioning (DP) offshore vessel, that is doing offshore operation such as on-loading and off-loading, drilling, oil producing, etc., occasionally faces significant changes of environmental force due to changes of wind, wave, and current condition in the ocean. In this situation, one possible scenario is that the vessel changes its heading without change of controlled position reducing the environmental load acting on the DP vessel. This function of DP vessels is called as weathervaning operation. In this paper, a new method of weathervaning control algorithm without any measurement for wind, wave, and current, so called a task space based weathervaning control algorithm, is introduced. The proposing control algorithm is formulated in a task space which is related with the control objective point on the DP vessel. And Lyapunov stability theory is considered in the formulation of nonlinear controller to achieve global stability. A set of experiments and simulations is designed to demonstrate the performance of the proposing task space based weathervaning control algorithm for DP vessels under significant changes of environmental condition on the ocean.