In this paper, convection heat transfer of Al2O3-water nanofluid turbulent flow through internally ribbed tubes with different rib shapes (rectangular, trapezoidal and semi-circular) is numerically investigated. For each rib shape, the optimum geometric ratio and volume fraction were calculated using entropy generation minimization technique. The governing equations in steady state and axisymmetric form have been solved using Finite Volume Method (FVM) with the SIMPLE algorithm. A uniform heat flux was applied on the wall. A single-phase approach has employed to model the nanofluid. Nanoparticles size is 20 nm and nanoparticles volume fraction and Reynolds number were within the ranges of 0-5% and 10,000-35,000 respectively. Comparisons between the numerical results and experimental data show that among different turbulence models, k-ε model with enhanced wall treatment gives better results. The results indicate that the heat transfer increases with nanoparticles volume fraction and Reynolds number but it is accompanied by increasing pressure drop. The simulations demonstrate that trapezoidal and semi-circular ribbed tubes have higher Nusselt number than the rectangular ribbed tubes with the same diameters. Correlations of heat transfer have obtained for different ribbed tubes. In evaluation of thermal performance and pressure drop, it is seen that the ribbed tubes with Al2O3-water nanofluid flow are thermodynamically advantageous. For each rib shape, the optimum geometric ratios are also presented.