We propose and demonstrate a Hilbert Superposition (HS) scheme in an optical single side-band (SSB) modulation and direct-detection system. The optical SSB signal is generated by a relatively low-cost dual-drive Mach-Zehnder modulator (DDMZM) biased at the quadrature point. The two driving signals are a pair of Hilbert signals with Nyquist pulse-shaped four-level pulse amplitude modulation (NPAM-4). In addition to the transmitted signal, both its Hilbert transform and the signal-to-signal beating interference (SSBI) can also be detected by the direct-detection, which introduce the interference to the transmitted signal. We use the HS before demodulation in the receiver to cancel the unwanted Hilbert transform term signal and deduct the SSBI to mitigate the nonlinear distortion. We demonstrate that the optical SSB NPAM-4 signal of 100 Gb/s over 80 km standard single mode fiber (SSMF) with bit error rate (BER) at 2.4×10−3 by simulation and 25 Gb/s signal with BER at 1.3×10−4 after 80 km transmission by experiment, respectively. We also find that the complexity of the equalization operation is reduced after HS.