The optical single sideband (SSB) transmitter based on dual modulation of an electro-absorption modulation laser (D-EML) has attracted considerable attention for its capability of monolithic integration and high output power. A model-based modulation method has been developed recently for generating high-quality optical SSB signals with this D-EML scheme. However, this method requires accurate characterization of the EML's chirps and pre-compensation for frequency responses of all-optical/electrical components, as well as the path difference between two driving signals. This imposes notable requirements on the transmitter characterization in practical applications. In this paper, we propose an adaptive method to approach the required responses of the pre-compensation filters for this optical SSB transmitter. This method avoids cumbersome device characterization and shows great resilience to the variation of system parameters. By using the proposed adaptive method, we generate a 56 Gb/s optical SSB orthogonal frequency-division multiplexed signal with the sideband suppression power ratio exceeding 21 dB. It is convenient with this method to switch the devices, i.e., directly modulated laser (DML) or electro-absorption modulator (EAM), to be pre-compensated for the optical SSB signal generation. Moreover, this method exhibits good tolerance to the path delay (±15 ps) between DML and EAM, as well as modulation depth. We also successfully transmit this signal over 80 km long standard single-mode fiber.