In this letter, the impact of residual hardware impairment (RHI) on the performance of non-orthogonal multiple access (NOMA) is investigated by taking into account the effect of imperfect successive interference cancellation (ipSIC). The new exact and asymptotic pairwise error probability (PEP) expressions with RHI under ipSIC are derived over Rayleigh fading channels. The asymptotic PEP expression is subsequently utilized to quantify the diversity orders achieved by NOMA users in the presence of RHI. In particular, we show that the effective diversity order of each NOMA user equals to user’s order for both ideal and non-ideal (RHI) scenarios. Leveraging the derived PEP, the union bound on the bit error rate of NOMA users are further evaluated. We demonstrate that the impact of RHI with ipSIC on each user’s error rate performance is negligible. In contrast, when perfect SIC is considered, such effects are significant. Numerical and Monte Carlo simulation results are presented to corroborate the analysis.