Existing 3D human pose estimators face challenges in adapting to new datasets due to the lack of 2D-3D pose pairs in training sets. To overcome this issue, we propose \textit{Multi-Hypothesis \textbf{P}ose \textbf{Syn}thesis \textbf{D}omain \textbf{A}daptation} (\textbf{PoSynDA}) framework to bridge this data disparity gap in target domain. Typically, PoSynDA uses a diffusion-inspired structure to simulate 3D pose distribution in the target domain. By incorporating a multi-hypothesis network, PoSynDA generates diverse pose hypotheses and aligns them with the target domain. To do this, it first utilizes target-specific source augmentation to obtain the target domain distribution data from the source domain by decoupling the scale and position parameters. The process is then further refined through the teacher-student paradigm and low-rank adaptation. With extensive comparison of benchmarks such as Human3.6M and MPI-INF-3DHP, PoSynDA demonstrates competitive performance, even comparable to the target-trained MixSTE model\cite{zhang2022mixste}. This work paves the way for the practical application of 3D human pose estimation in unseen domains. The code is available at https://github.com/hbing-l/PoSynDA.