In this letter, a hybrid orthogonal frequency-division multiplexing (OFDM)-based modulation technique for narrowband Internet of Things (NB-IoT) is introduced and analyzed. The technique combines fast-OFDM with index modulation in order to maximize bandwidth and power efficiency for IoT applications. The ideal number of active subcarriers to maximize spectral efficiency is derived. The one-dimensional constellation used in fast-OFDM is also optimized to enhance error performance of the proposed system. Numerical results indicate that the proposed system outperforms other OFDM systems based on index modulation in the relatively low signal-to-noise ratio (SNR) region, while it provides additional design options for trading off power efficiency and spectral efficiency in the higher SNR region.