A new high-efficient method for measuring isotope shifts and hyperfine structures in optical transitions of radioactive atoms is described. The method is based on application of laser resonance ionization in a mass separator ion source. The high sensitivity of the method results from a high efficiency of the laser ion source and a low background of the detection system, which uses counting α-particles following the decay of the isotope under investigation. The isotope shifts and hyperfine structures for ^154-156Yb in the 555.6 nm transition have been measured. It is shown that in a number of cases this method allows measurements to be carried out for isotopes with a production rate in the target down to 1-10 atoms per second.