Retargeting human motion to humanoid robots is critical for teleoperation, imitation learning and human-robot interaction. However, it remains challenging because of substantial morphological discrepancies between humans and robots, including differences in skeletal topology, limb proportions and degrees of freedom, as well as the scarcity of paired motion data. This paper presents Human2Humanoid, an unsupervised motion retargeting framework that transfers human motions to humanoid robot behaviors with high fidelity. To bridge the domain gap under unpaired data, we adopt a CycleGAN-based architecture equipped with a skeleton-aware graph convolutional network to capture topology-dependent motion features. To address cross-domain scale mismatches, we introduce a morphology-invariant end-effector consistency loss that aligns normalized end-effector trajectories to preserve motion semantics across embodiments. To improve physical plausibility and reduce contact artifacts, we impose explicit physics-aware feasibility constraints to encourage reproduction of the contact patterns in the source motion. Experimental results show that the proposed method successfully retargets human motion to the Unitree G1 humanoid robot without paired data, and outperforms existing methods in both downstream controllability and physical feasibility.