A new, efficient potential model for liquid water is presented here. It is based on the hard-sphere sticky dipole potential model for water by Bratko, Blum, and Luzar (J. Chem. Phys. 1985, 83, 6367), referred to as the BBL model. Similar to the BBL model, this new, soft-sphere sticky dipole model has a single interaction site at the molecular center of mass with a spherical repulsive potential, a short-range tetrahedral "sticky" potential, and a point dipolar potential. However, the use of a Lennard-Jones-type soft-sphere, as opposed to the hard-sphere in the BBL model, allows realistic studies of water and aqueous solvation. This is particularly important for the existing parametrizations of biological molecules that use soft-sphere models. The present model gives a liquid water structure comparable to that found by the four-site TIP4P model and also gives an intermolecular energy, a hydrogen bond energy, and a heat capacity of liquid water in good agreement with experimental data and/or results from the TIP3P or the TIP4P model. In addition, Monte Carlo simulations using this model are nearly an order of magnitude faster than those using the TIP3P or TIP4P model. Monte Carlo simulations have also been carried out to study the solvation of a single Na+ or Cl- ion at room temperature, using a hybrid scheme in which the ion-water interaction is modeled by monopole-dipole plus monopole-quadrupole potentials and the water-water interaction is modeled by this new model. The calculated structure of water around the ion and the enthalpy of ionic solvation are in good agreement with those from experiments and from simulations using other water models. Overall, the simplicity, efficiency, and reasonable accuracy of this model make it potentially very useful for studies of aqueous solvation by either computer simulations or integral equation theories.