For optimal design of a gas-cooled reactor, pumping power can be improved by flattening the axial temperature distribution of the fuel elements. The optimization of pumping power for a single fuel element with annular passage and uniform heat flux or pseudo-sinusoidal heat flux is examined first. When the dimensionless highest wall temperature θ h is given, the optimal dimension of the channel at which pumping power becomes minimum may be obtained. Furthermore, axial temperature distribution of a single fuel element can be flattened by varying the cross-sectional area of the coolant passage. The pumping power can be less than the least pumping power of a straight annulus.