In systems that aim to mitigate the inter-carrier interference (ICI) caused by doubly selective (DS) channels, the partial Fast Fourier Transform (PFFT) has emerged as an interesting alternative to the conventional FFT. In this letter, we propose a novel PFFT demodulation scheme based on fast convolution (FC) structure. The proposed scheme uses the overlap-save operation of FC to further suppress the residual interference (RI) to improve performance over DS channels, including in terms of bit error rate (BER), while, at the same time, allowing for an improvement in spectral efficiency by avoiding the use of a cyclic prefix (CP). We provide a theoretical analysis of RI and numerical simulations to demonstrate the superiority of the proposed scheme in terms of BER performance.