This paper presents a novel method to generate a localized mode single-carrier frequency division multiple access (SC-FDMA) waveform. Instead of using DFT-spread OFDMA (DFT-S-OFDMA) processing, the new structure called SCiFI-FDMA relies on frequency and time domain interpolation followed by a user-specific frequency shift. SCiFI-FDMA can provide signal waveforms that are compatible to DFT-S-OFDMA. In addition, it provides any resolution of user bandwidth allocation for the uplink multiple access with comparable computational complexity, because the DFT is avoided. Therefore, SCiFI-FDMA allows a flexible choice of parameters appreciated in broadband mobile communications in the future.