We propose a simple united-atom second-order potential model for dimethylmethylphosphonate (DMMP) designed to reproduce molecular conformations and physical properties, such as the liquid density, heat of evaporation, and thermal expansion coefficient of the pure liquid. By use of the model, we explore molecular structure, thermodynamic characteristics, and dynamic properties of liquid DMMP and its aqueous solutions by molecular dynamics simulations. It is shown that accurate choice of partial atomic charges is of crucial importance for a correct description of phase behavior and physical properties of aqueous solutions of alkylphosphonates. The excess volume and the enthalpy of mixing in a DMMP-water system were found negative with a minimum presumably located within the concentration range between 33 and 50% volume. On average, one DMMP molecule forms two hydrogen bonds with surrounding water via the oxygen atom that forms a double bond to phosphorus. The average lifetime of hydrogen bonds does not exceed rotation correlation time of individual water molecule, thus indicating that there are no long-living DMMP.H2O complexes in the aqueous solutions.