This paper proposes a new linear precoding scheme for downlink transmission in MIMOME channels, referred to as secure regularized zero forcing. The scheme modifies regularized zero forcing precoding, such that the beamformers further suppress the information leakage towards the eavesdroppers. The proposed scheme is characterized in the large-system limit, and a closed-form expression for the achievable ergodic secrecy rate per user is derived. Numerical investigations demonstrate high robustness against the quality of eavesdroppers' channel.