A Z-pinch dynamic hohlraum can create the high-temperature radiation field required by indirect-drive inertial confinement fusion. A dynamic hohlraum with peak radiation temperature over 300 eV can be obtained with a $>$50 MA Z-pinch driver according to the scaling law of dynamic hohlraum radiation temperature vs drive current. Based on a uniform 300 eV radiation temperature profile with a width of 10 ns, three double-shell capsules with radii of 2, 2.5, and 3 mm are proposed, and the corresponding fusion yields from a one-dimensional calculation are 28.8, 56.1, and 101.6 MJ. The implosion dynamics of the 2.5 mm-radius capsule is investigated in detail. At ignition, the areal density of the fuel is about 0.53 g/cm², the fuel pressure is about 80 Gbar, and the central ion temperature is about 4.5 keV, according to the one-dimensional simulation. A two-dimensional simulation indicates that the double-shell capsule can implode nearly spherically when driven by the radiation field of a Z-pinch dynamic hohlraum. The sensitivities of the fusion performance to the radiation temperature profiles and to deviations in the capsule parameter are investigated through one-dimensional simulation, and it is found that the capsule fusion yields are rather stable in a quite large parameter space. A one-dimensional simulation of a capsule embedded in 50 mg/cm³ CH foam indicates that the capsule performance does not change greatly in the mimicked environment of a Z-pinch dynamic hohlraum. The double-shell capsules designed here are also applicable to laser indirect-drive inertial fusion, if a laser facility can produce a uniform 300 eV radiation field and sustain it for about 10 ns.