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Frequency-domain pre-equalization (pre-FDE) can improve the single-carrier (SC) signal transmission performance in a severe frequency-selective channel. However, the performance improvement is limited by the residual inter-symbol interference (ISI). The residual ISI can be eliminated by the joint use of Tomlinson-Harashima precoding and frequency-domain pre-equalization (called joint THP/pre-FDE) and its performance improvement was confirmed by computer simulation. In this paper, we present a theoretical analysis of joint THP/pre-FDE. The conditional bit error rate (BER) for the given channel realization is derived by taking into account the modulo operation error in a receiver and the achievable BER performance is numerically evaluated.