Recovering 3D human poses from a monocular camera view is a highly ill-posed problem due to the depth ambiguity. Earlier studies on 3D human pose lifting from 2D often contain incorrect-yet-overconfident 3D estimations. To mitigate the problem, emerging probabilistic approaches treat the 3D estimations as a distribution, taking into account the uncertainty measurement of the poses. Falling in a similar category, we proposed FMPose, a probabilistic 3D human pose estimation method based on the flow matching generative approach. Conditioned on the 2D cues, the flow matching scheme learns the optimal transport from a simple source distribution to the plausible 3D human pose distribution via continuous normalizing flows. The 2D lifting condition is modeled via graph convolutional networks, leveraging the learnable connections between human body joints as the graph structure for feature aggregation. While trade-offs between processing time and precision exist, already in the equal-accuracy comparison, FMPose exhibits significantly faster processing time than the diffusion model, and also offers another faster and more accurate configuration. Experimental results show major improvements of our FMPose over current state-of-the-art methods on two common benchmarks for 3D human pose estimation, namely Human3.6M, MPI-INF-3DHP. Additionally, FMPose shows competitive performance on the more challenging 3DPW dataset. The code implementation is available at https://github.com/cuongle1206/FMPose