In this paper, we propose a real-valued interleaved single-carrier frequency-division multiplexing (I-SC-FDM) scheme for intensity-modulation and direct-detection optical interconnects. By simplifying the encoding structure, the computational complexity can be reduced from Nlog2N complex multiplications to N complex multiplications. At the complementary cumulative distribution function of 10-2, a reduction of 10 dB and 7.5 dB for the peak-to-average power ratio (PAPR) of the I-SC-FDM is achieved than that of orthogonal frequency-division multiplexing modulated with QPSK and 16QAM, respectively, when the subcarrier number is set to 4096. We experimentally demonstrate the I-SC-FDM scheme for optical interconnects with data rates of 12 Gbit/s, 24 Gbit/s and 128 Gbit/s transmitted over 22.5-km, 22.5-km and 2.4-km standard single mode fiber, respectively. The I-SC-FDM scheme shows great potential for cost-sensitive and power-sensitive optical interconnects owing to its low computational complexity and low PAPR.