The creep and recovery of metallic glasses exhibit pronounced asymmetric evolution, challenging the conventional anelastic assumption of time-reversal symmetry. We establish a two-level hierarchical anelastic constitutive model for a La₂₅Ce₂₅Ni₁₀Co₂₀Al₂₀ metallic glass over 423–463 K and 20–100 MPa, decomposing anelastic strain into fast and slow relaxation units. The model captures the entire creep-recovery response with high fidelity. During creep, the fast unit activates first and triggers the slow one. Upon unloading, the slow unit recovers almost fully and rapidly, while the fast unit recovers only partially. The activation energy of the fast unit during creep decreases from 0.59 to 0.26 eV with increasing stress, with an activation volume of 0.7 nm³. Its recovery activation volume (0.91 nm³) exceeds the forward value, indicating more cooperative reverse motion. To unveil the microscopic origin, we correlate recovery coefficient with the potential energy landscape. The fast unit is trapped in a rough sub-basin with numerous metastable lock-in states. Statistical analysis yields the number of locked states M ≈ 8–35 and an energy barrier difference of 0.16 eV between reversible and locked pathways, consistent with sub-basin rugosity. Differential scanning calorimetry independently verifies the locked states via relaxation enthalpy measurements, with the irreversible enthalpy fraction decreasing monotonically with recovery coefficient. This work provides a thermodynamically consistent framework linking macroscopic anelasticity to potential energy landscape topology, offering a quantitative tool for evaluating structural stability of metallic glasses under service loading.