A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Eulerian-Lagrangian formulation is adopted and a higher-order boundary element method in conjunc-tion with an image Green function is used for the fluid domain. The boundary values on the free surface are updated at each time step by a fourth-order Ranga-Kutta time-marching scheme at each time step. Input wave characteristics are specified at the upstream boundary by an appropriate wave theory. At the downstream boundary, an artificial damping zone is used to prevent wave reflection back into the computational domain. Using the image Green function in the whole fluid domain, the integrations on the two lateral walls and bottom are excluded. The simulation results on extreme wave elevations in finite and infinite water-depths are compared with experimental results and second-order analytical solutions respectively. The wave kinematics is also discussed in the present study.