To increase the reliability of auto-ignition in CAI engines, the thermodynamic properties of intake flow is often controlled using recycled exhaust gases, called internal EGR. Because of the internal EGR influence on the overall thermodynamic properties and mixing quality of the gases that affect the subsequent combustion behavior, optimizing the intake and exhaust valve timing for the EGR is important to achieve the reliable auto-ignition and high thermal efficiency. In the present study, fully 3D numerical simulations were carried out to predict the mixing characteristics and flow field inside the cylinder as a function of valve timing. The 3D unsteady Eulerian-Lagrangian two-phase model was used to account for the interaction between the intake air and remaining internal EGR during the under-lap operation while varying three major parameters: the intake valve(IV) and exhaust valve(EV) timings and intake valve lift(IVL). Computational results showed that the largest EVC retardation, as in A6, yielded the optimal mixing of both EGR and fuel. The IV timing had little effect on the mixing quality. However, the IV timing variation caused backflow from the cylinder to the intake port. With respect to reduction of heat loss due to backflow, the case in B6 was considered to present the optimal operating condition. With the variation of the intake valve lift, the A1 case yielded the minimum amount of backflow. The best mixing was delivered when the lift height was at a minimum of 2 mm.