The poor generalizability of intravascular ultrasound (IVUS) analysis methods caused by the great diversity of IVUS datasets is hopefully addressed by the domain adaptation strategy. However, existing domain adaptation models underperform in intravascular structural preservation, because of the complex pathology and low contrast in IVUS images. Losing structural information during the domain adaptation would lead to inaccurate analyses of vascular states. In this paper, we propose a Multilevel Structure-Preserved Generative Adversarial Network (MSP-GAN) for transferring IVUS domains while maintaining intravascular structures. On the generator-discriminator baseline, the MSP-GAN integrates the transformer, contrastive restraint, and self-ensembling strategy, for effectively preserving structures in multi-levels, including global, local, and fine levels. For the global-level pathology maintenance, the generator explores long-range dependencies in IVUS images via an incorporated vision transformer. For the local-level anatomy consistency, a region-to-region correspondence is forced between the translated and source images via a superpixel-wise multiscale contrastive (SMC) constraint. For reducing distortions of fine-level structures, a self-ensembling mean teacher generates the pixel-wise pseudo-label and restricts the translated image via an uncertainty-aware teacher-student consistency (TSC) constraint. Experiments were conducted on 20MHz and 40MHz IVUS datasets from different medical centers. Ablation studies illustrate that each innovation contributes to intravascular structural preservation. Comparisons with representative domain adaptation models illustrate the superiority of the MSP-GAN in the structural preservation. Further comparisons with the state-of-the-art IVUS analysis accuracy demonstrate that the MSP-GAN is effective in enlarging the generalizability of diverse IVUS analysis methods and promoting accurate vessel and lumen segmentation and stenosis-related parameter quantification.