A new technique is described which allows Doppler-free, isotope-selective excitation of atoms by continuous wave laser radiation and continuous ionization of the atoms by an electric field. The atoms are excited to high Rydberg states in an electric-field-free region of a collimated atomic beam. Because the lifetimes of Rydberg atoms are long they can reach a spatially separated region of the atomic beam where they are ionized by a continuous electric field with a probability of unity. In the case of lithium we obtained a 103 times larger ion signal by field ionization of Rydberg atoms than by direct photoionization from low excited states.