We present a global nonlocal and dispersive optical model potential for neutron scattering off spherical nuclei with incident energies up to 250 MeV. This optical model is an extension of the non-dispersive Perey-Buck potential. The imaginary components are chosen energy-dependent and the dispersive constraints are taken into account. The surface imaginary part is nonlocal, whereas the volume imaginary part above 10 MeV is local, allowing to reproduce total cross sections and scattering data for high energies. We obtain a good description of scattering observables for target-nuclei ranging from $A=16$, up to $209$. The inclusion of nonlocal spin-orbit term enables a better description of the analyzing power data relative to the local dispersive model.