The convective heat transfer and entropy generation characteristics of Ag-MgO/water hybrid nanofluid flow through rectangular minichannel were numerically investigated. The Reynolds number was in the range of 200 to 2000 and different nanoparticle volume fractions were varied between phi = 0.005 and 0.02. In addition, Artificial Neural Network was used to create a model for estimating of entropy generation of Ag-MgO/water hybrid nanofluid flow. As a result, it was found that the convective heat transfer coefficient for phi = 0.02 Ag-MgO/water hybrid nanofluid is 21.29% higher than that of pure water, at Re=2000. Total entropy generation of Ag-MgO/water hybrid nanofluid increased with increasing nanoparticle volume fraction. The results obtained by ANN showed good agreement with the numerical results obtained in this study.