Spectral-domain optical coherence tomography (SD-OCT) images inevitably suffer from multiplicative speckle noise caused by random interference. This study proposes an unsupervised domain adaptation approach for noise reduction by translating the SD-OCT to the corresponding high-quality enhanced depth imaging (EDI)-OCT. We propose a structure-persevered cycle-consistent generative adversarial network for unpaired image-to-image translation, which can be applied to imbalanced unpaired data, and can effectively preserve retinal details based on a structure-specific cross-domain description. It also imposes smoothness by penalizing the intensity variation of the low reflective region between consecutive slices. Our approach was tested on a local data set that consisted of 268 SD-OCT volumes and two public independent validation datasets including 20 SD-OCT volumes and 17 B-scans, respectively. Experimental results show that our method can effectively suppress noise and maintain the retinal structure, compared with other traditional approaches and deep learning methods in terms of qualitative and quantitative assessments. Our proposed method shows good performance for speckle noise reduction and can assist downstream tasks of OCT analysis.