Numerical investigation of a 80°swept delta wing rock characteristics was presented by solving N-S (Navier-Stokes) equations coupled with Euler rigid-body dynamics equations, and the influences of leading edge configuration and roll-axis installation were discussed. For the unsteady simulation of self-induced wing rock phenomenon, the Roe scheme and LU-SGS method with dual-time stepping approach were employed for NS equations discretization, the second order differential scheme was employed for Euler rigid-body equation discretization, and the loose-coupling approach for flow control equations and movement control equations was implemented. For the delta wing with a roll-axis located on the upper surface, three leading edge configurations, including upper beveled, lower beveled and double beveled were used for evaluating the influence on the amplitudes and bifurcation angles of delta wing rock. In view of the configuration equivalence of upper beveled delta wing and lower beveled delta wing, the influence of roll-axis installation was evaluated also. The results show that under a certain attack angle, all of the three delta wings with different leading edge configuration establish large and self-retained wing rock amplitudes, and the largest amplitude is observed with upper beveled delta wing, the double beveled delta wing takes the second place and the amplitude of lower beveled delta wing reaches the least degree. For the attack angle of 30°, the roll-over phenomena are observed at the delta wings with upper and double beveled leading edge configuration, and when the roll angle reaches to 180°, the oscillation amplitude remains unchanged.