A new apparatus has been constructed for high‐precision hyperfine structure measurement of atomic ions by laser‐radio‐frequency double‐resonance technique involving a slow ion beam and a laser in collinear geometry. The low ion energy (1–1.5 keV) leads to longer interaction time with the applied rf field. Consequently, extremely narrow linewidths of ∼60 kHz have been observed for the first time in such systems. The apparatus has been used for the measurement of hyperfine structure of the 4f7(8S0)5d9D02,3,4,5metastable levels in151Eu+and153Eu+. The magnetic dipole and the electric quadrupole hyperfine constants,AandB, respectively, have been determined with higher precision (2–3 orders of magnitude).