Equilibrium and nonequilibrium molecular-dynamics simulations of the central force model of water (CFM) [Lemberg and Stillinger, J. Chem. Phys. 62, 1677 (1975)] are presented. We consider a model based on a functional form introduced in theoretical studies of associating systems employing integral equations [F. Bresme, J. Chem. Phys. 108, 4505 (1998)]. Results on thermodynamic, dynamic, dielectric, and coexistence properties are presented. The central force model shows satisfactory agreement with the experimental results in all these cases. In addition, nonequilibrium molecular-dynamics simulations show that the CFM predicts a decrease of the thermal conductivity with temperature, as observed in the experiment, but this dependence is reproduced qualitatively at temperatures characteristic of supercooled states. These results emphasize the need for further studies of the heat conduction and properties of water in these conditions. Overall the present potential should provide a basis for further theoretical and simulation studies of complex systems where water is present.