A new electron-water molecule pseudopotential is developed and tested in the present paper. The formal development of the potential is based on our earlier quantum mechanical model calculations of the excess electronic states of the electron-water molecule system [Turi , J. Chem. Phys. 114, 7805 (2001)]. Although the new pseudopotential has a very simple analytical form containing only nine adjustable parameters, it reproduces the exact eigenvalue of the excess state and the electron density of the smooth pseudo-wave function in the static-exchange limit. Of the individual potential energy terms, one can extract the exact electrostatic, the local repulsion and, as the remaining part, the local exchange potentials. The polarization term is added to the potential a posteriori. The most important feature of the potential is that the repulsive core region of the potential is finite and relatively narrow. This property leads to the non-negligible penetration of the excess electron in the core. The attractive wells of the potential also appear significantly closer to the nuclei than in previous pseudopotentials. The new pseudopotential is tested in quantum molecular dynamics simulations of a ground-state excess electron in a water bath. Whereas the basic features of the equilibrium hydrated electron are similar to those predicted in earlier simulations, important quantitative details are significantly improved relative to available experimental data. In particular, the simulations reproduce the equilibrium ground state energy and the optical absorption spectrum quite well. The differences of the present pseudopotential from previous works are also manifested in the more diffuse ground-state electron distribution and the more compact solvation structure. Further structural and dynamical consequences of the application of the new pseudopotential are analyzed in detail.