This paper presents the performance analysis of two users’ downlink non-orthogonal multiple access (NOMA) over a millimeter-wave two-wave with diffuse power (TWDP) fading model for successive interference cancellation errors. The new closed-form expressions of average bit error probability (ABEP) for both users are derived for quadrature phase-shift-keying and binary phase-shift-keying modulation pairs. Further, the asymptotic ABEP expressions are derived to provide better insights into the performance analysis. The diversity order of each user is also derived with the aid of asymptotic ABEP expression. The obtained expressions over TWDP fading channels are generalized ABEP expressions as it also shows ABEP expressions for both Rician and Rayleigh fading channels as special cases. Simulation results support the correctness of each analytical ABEP expression.