The evolution of 5G wireless networks poses significant research challenges such as securing the user data, maintaining certain latency and reliability requirements etc. However, it can be challenging to simultaneously meet these performance requisites, which may lead to resort to a trade-off among different metrics. This paper investigates the secrecy-reliability performance trade-off (SRPT) for non-orthogonal multiple access (NOMA)-based millimeter wave (mmWave) networks. Herein, we consider two end-users, namely primary and secondary, which are served by an mmWave base station using downlink NOMA. Besides, a passive eavesdropper lying in the vicinity of these endusers attempts to intercept their legitimate message signals. For this set-up, we derive the closed-form expressions of the outage probability (OP) of a targeted end-user and intercept probability (IP) of the eavesdropper to analyze the SRPT of the system. We further propose a low-complexity average channel state information (CSI)-based power allocation strategy to improve the reliability of a targeted user while maintaining its information secrecy. Moreover, we obtain the condition under which NOMA guarantees superior secrecy performance than that of orthogonal multiple access (OMA) scheme. We corroborate our theoretical analysis via simulation results presented in terms of IP and OP.