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. Plain Language Summary: Although many geodynamic mechanisms have been proposed regarding the origin of the observed complex structure of Earth's inner core, no clear consensus has been reached. This is partly owing to the lack of accurate knowledge of the viscosity in the inner core, which is believed to mostly comprise of hexagonal close‐packed Fe (hcp‐Fe). Here, we studied the viscosity of hcp‐Fe using high‐pressure and high‐temperature deformation experiments. The results showed that the dominant deformation mechanism in hcp‐Fe changes depending on the temperature, with power‐law dislocation creep and low‐temperature creep being most important above and below ∼800 K, respectively. Based on extrapolation of these experimental results we estimate the inner core viscosity to be ≥1019 Pa s. This inner core viscosity suggests the equatorial growth or translation mode model as the dominant geodynamical mechanism in the Earth's inner core. Key Points: We studied rheology of hexagonal close‐packed Fe based on high‐pressure and high‐temperature deformation experimentsDominant deformation mechanism was power‐law dislocation creep at temperatures above ∼800 KWe estimated the viscosity of hexagonal close‐packed Fe under inner core conditions as ≥∼1019 Pa s [ABSTRACT FROM AUTHOR]