FTN signalling is an effective communication method that achieves a high spectral efficiency. However, employing a symbol rate faster than the Nyquist rate disrupts the orthogonality between symbols, leading to unavoidable inter-symbol interference (ISI). To mitigate the effects of ISI, interference cancellation and signal detection processes are essential for FTN receivers. Conventional ISI reduction techniques often utilize trellis-based algorithms. However, as the number of states increases due to additional interference symbols, the complexity of these algorithms grows exponentially. To address this challenge, this paper explores a matrix computation-based interference cancellation technique tailored for FTN communication systems, aiming to significantly reduce the complexity of the ISI mitigation process. To execute ISI cancellation and signal detection more precisely, the proposed technique includes iterative interference cancellation and a signal detection process. When six interference symbols are considered, the complexity of the proposed technique is reduced by 97% compared with that of the conventional Viterbi algorithm. Furthermore, in the case of τ = 0.85, the performance of the proposed technique is about 1 dB better than that of the Viterbi algorithm at BER = 10−4.