Slosh phenomena are being encountered in various fields leading to performance deterioration. The major challenges in slosh control are due to underactuated nature. Moreover, it is very difficult to measure the slosh angle, which poses additional challenge. In this paper, a control approach for container-slosh system is discussed using output-feedback. To make the controller robust and practically implementable higher order sliding mode (HOSM) scheme is used. Surface is a linear combination of displacement and velocity of the container. Control is developed using second-order sliding modes (SOSM) based on super-twisting algorithm. Closed-loop stability has been verified mathematically using Lyapunov approach. Finally, the performance of the controller is validated in simulations.