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The viscosity of hexagonal close‐packed (hcp) Fe is a fundamental property controlling the dynamics of the Earth's inner core. We studied the rheology of hcp‐Fe using high‐pressure and ‐temperature deformation experiments with in situ stress and strain measurements. Experiments were conducted using D111‐type and deformation‐DIA apparatuses at pressures of 16.3–22.6 GPa, temperatures of 423–923 K, and uniaxial strain rates of 1.52 × 10−6 to 8.81 × 10−5 s−1 in conjunction with synchrotron radiation. Experimental results showed that power‐law dislocation creep with a stress exponent of n = 4.0 ± 0.3, activation energy of E* = 240 ± 20 kJ/mol, and activation volume of V* = 1.4 ± 0.2 cm3/mol is dominant deformation mechanism at >∼800 K, whereas a mechanism with power‐law breakdown prevails at lower temperatures. An extrapolation of the power‐law dislocation creep flow law based on homologous temperature scaling suggests the viscosity of hcp‐Fe under inner core conditions is ≥∼1019 Pa s. If this power‐law dislocation creep mechanism is assumed to be the dominant mechanism in the Earth's inner core, the equatorial growth or translation mode mechanism may be the dominant geodynamical mechanism causing the observed inner core structure.