Molecular dynamics simulations of mixtures of N,N-dimethylformamide (DMF) with water of various compositions, covering the entire composition range, are performed on the canonical (N,V,T) ensemble. The local structure of the mixtures is analyzed in terms of radial distribution functions and the contributions of the first five neighbors to them, various order parameters of the water molecules around each other, and properties of the Voronoi polyhedra of the molecules. The analyses lead to the following main conclusions. The two molecules are mixing with each other even on the molecular scale; however, small self-aggregates of both components persist even at their small mole fraction values. In particular, water-water H-bonds exist in the entire composition range, while water clusters larger than 3 and 2 molecules disappear above the DMF mole fraction values of about 0.7 and 0.9, respectively. The O atoms of the DMF molecules can well replace water O atoms in the hydrogen-bonding network. Further, the H-bonding structure is enhanced by the presence of the hydrophobic CH3 groups of the DMF molecules. On the other hand, the H-bonding network of the molecules gradually breaks down upon the addition of DMF to the system due to the lack of H-donating groups of the DMF molecules. Finally, in neat DMF, the molecules form weak, CH-donated H-bonds with each other; however, these H-bonds disappear upon the addition of water due to the increasing competition with the considerably stronger OH-donated H-bonds DMF can form with the water molecules.