In the single-carrier (SC) transmission, minimum mean square error frequency-domain equalization (MMSE-FDE) can achieve a good bit error rate (BER) performance in a frequency-selective fading channel. The conventional FDE requires the insertion of cyclic prefix (CP) to make the received signal block to be a circular convolution of the transmit signal and the channel. Overlap FDE requires no CP insertion. However, its BER performance improvement is limited by the residual inter-block interference (IBI). In this paper, we present the theoretical analysis of the BER performance achievable with overlap FDE by taking into account the residual IBI after overlap FDE. Then, by using the Gaussian approximation of the residual IBI as well as the residual inter-symbol interference (ISI), we derive the conditional BER for the given set of the channel gains. The average BER performance is numerically evaluated.