The liquid metal turbulent heat transfer in eccentric annuli was numerically calculated without introducing the turbulent Prandtl number for the case when the inner cylinder is heated with uniform heat flux. An algebraic Reynolds stress model of turbulence was employed to calculate Reynolds normal and shear stresses. The distributions of turbulent heat fluxes in a cross section were evaluated by simultaneously solving simple forms of algebraic equations, which were derived from the governing equations of turbulent heat fluxes under the local equilibrium assumption. Discussions were given in the cross-sectional distributions of averaged velocity and turbulence intensity, and on the peripheral average of local Nusselt number. The results obtained were found reasonable. The discrepancy found between the present computation and available experimental data was discussed and concluded to originate from the difference between the conjugate thermal boundary condition realized in the experiments and the simpler one adopted in the present computation.