Spillways play an important role in the safety of dams. To ensure the safety of dams, spillways should be designed considering floods with long return periods. To increase the discharge capacity of a spillway, a designer can increase the crest length using the labyrinth spillway. For high head conditions, the local submergence may decrease the efficiency of a labyrinth spillway. In this study, the hydraulic characteristics of linear and arced labyrinth spillways are compared and the effect of the downstream bed level on the discharge coefficient of labyrinth spillways is studied numerically. The numerical simulations are done using Flow-3D software. RNG k-ε model is used for turbulence simulations and the free surface profiles are calculated by VOF method. Experimental data of pervious researchers are used for validation of the proposed numerical model. The results show that in the high head conditions, lowering the downstream bed level of a labyrinth spillway increases its efficiency, especially in the case of an arced labyrinth spillway.