In this paper, a novel spectrum efficient single-sideband single-carrier (SC) with frequency-domain equalization (SSB-FDE) using amplitude shift keying (ASK) modulation (ASK SSB-FDE) is proposed. Similar to the conventional SC transmission with FDE (SC-FDE), the ASK modulated symbol block to be transmitted is transformed by discrete Fourier transform (DFT) into frequency-domain signal. Then, inverse DFT (IDFT) is applied to the upper (or lower) sideband spectrum to obtain the time-domain SSB signal block. The cyclic prefix (CP) inserted SSB signal block is transmitted over a frequency-selective fading channel. At a receiver, the minimum mean square error (MMSE) based FDE is applied. ASK SSB-FDE has lower peak-to-average power ratio (PAPR) and better throughput performance than QAM SC-FDE when the throughput is plotted as a function of peak transmit SNR. This is confirmed by computer simulation assuming a frequency-selective Rayleigh fading channel.