Wave glider is a novel autonomous surface vehicle that uses energy from surface waves for propulsion. However, because it is inherently under-actuated, multi-variable and strong coupled, it is challenging to control the wave glider accurately under the environmental disturbances. In this study, a novel robust position keeping guidance strategy and an advanced path following approach for the under-actuated wave glider based on restricted circle are firstly developed. Furthermore, an 8-DOFs (Degree-of-Freedom) mathematical model for the under-actuated wave glider is adopted, and the position keeping and path following tasks of the wave glider are conducted in simulation. The results demonstrate that the under-actuated wave glider is able to accomplish the position keeping and path following tasks with the proposed strategies.