This paper investigates the security enhancement of an intelligent reflecting surface (IRS) assisted non-orthogonal multiple access (NOMA) network, where a base station (BS) serves users securely with the assistance of distributed IRSs. Considering that eavesdropper’s instantaneous channel state information (CSI) is challenging to acquire in practice, we utilize secrecy outage probability (SOP) as the security metric. A problem of maximizing the minimum secrecy rate among users, by jointly optimizing transmit beamforming at the BS and phase shifts of the IRSs, is formulated. For a special case with a single-antenna BS, we derive the closed-form SOP expressions and propose a novel ring-penalty based successive convex approximation (SCA) algorithm to design transmit power and phase shifts jointly. For a general multi-antenna BS case, we develop a Bernstein-type inequality based alternating optimization (AO) algorithm to solve the challenging problem. Numerical results demonstrate the advantages of the proposed algorithms over the baseline schemes. The results show that: 1) the maximum secrecy rate is achieved when distributed IRSs share the reflecting elements equally; 2) the distributed IRS deployment does not always outperform the centralized IRS deployment, due to the tradeoff between the number of IRSs and the reflecting elements equipped at each IRS.