In this paper, we explore the physical-layer security of a multi-user wireless system that consists of multiple users intending to transmit to a base station (BS), while multiple eavesdroppers attempt to tap the user transmissions. We examine the employment of multi-user scheduling for improving the transmission security against eavesdropping and propose a multi-user scheduling scheme, which only requires the channel state information (CSI) of BS without the need of the passive eavesdroppers' CSI. We also consider the round-robin scheduling for comparison purposes. The closed-form secrecy outage probability expressions of the round-robin scheduling and proposed multi-user scheduling are derived over Rayleigh fading channels. Numerical results demonstrate that the proposed multi-user scheduling outperforms the round-robin scheduling in terms of the secrecy outage probability. As the number of users increases, the secrecy outage probability of round-robin scheduling keeps unchanged. By contrast, the secrecy outage performance of the proposed multi-user scheduling improves significantly with an increasing number of users.