The dual modulation transmitter, where both the directly modulated laser (DML) and electro-absorption modulator (EAM) are modulated, has attracted considerable attention due to its monolithic integration and high output power. This transmitter is capable of manipulating the optical intensity and phase independently since the DML and EAM serve mainly as phase and intensity modulators, respectively. Thus, the dual modulation scheme has been used to generate optical single sideband (SSB) signals. However, due to a lack of workable model applicable to high modulation frequency (e.g., >10 GHz), the data rates of optical SSB signals reported previously were all limited to <= 40 Gb/s. In this paper, we generate a 120-Gb/s optical SSB orthogonal frequency-division multiplexed (OFDM) signal using the dual modulation scheme. By using the time-harmonic model of dual modulation we have recently reported, we establish a generation procedure for broadband optical SSB signals, where the modulation conditions for DML and EAM are provided. In order to satisfy these conditions over a broad frequency range, we also propose (1) utilizing the frequency-modulation discriminator to measure the DML's chirp characteristics and (2) pre-compensating for the frequency responses of DML and EAM. In our experimental verification, we generate the 120-Gb/s SSB OFDM signal having an optical sideband suppression ratio of 19 dB. We also successfully transmit this signal over 80 km long standard single-mode fiber.