This paper considers a secure non-orthogonal multiple access system, where confidential messages are transmitted from a base station to multiple legitimate destinations and wiretapped by multiple illegitimate receivers. It is assumed that all the channels experience Nakagami-m fading model and all the nodes are equipped with multiple antennas, respectively. Both non-colluding and colluding eavesdroppers are respectively considered. Max-min (MM) transmit antenna selection (TAS) strategy is adopted to improve the secrecy performance of the target system, in which both users in user paring are considered simultaneously. In particular, closed-form expressions for the cumulative distribution function of the signal-to-interference-noise ratio at the legitimate user are derived firstly. Then we obtain the exact and asymptotic analytical results in a closed form for the secrecy outage probability of MM TAS scheme. Monte-Carlo simulation results are presented to corroborate the correctness of the analysis. The results show that the secrecy diversity order is zero and non-zero for fixed and dynamic power allocations, respectively.