Through the design strategy of equivalent metal-ion substitution, five sodium iodates containing heavy rare-earth elements, NaRE(IO3)4(RE=Dy, Ho, Er, Yb, Lu), were synthesized. Their crystal structures were determined using single crystal X-ray diffraction. These compounds are heterogeneous isomers with the same non-centrosymmetric monoclinic space group, Cc. The linear and nonlinear optical (NLO) properties as well as thermal stability were characterized by UV-Vis absorption spectroscopy, infrared spectroscopy, thermogravimetric analysis and second harmonic generation (SHG) measurement, respectively. The second-order NLO effects of these compounds are quite different and their SHG intensities are in the range of 0.1 to 3.3 times than that of KDP with phase-maching characteristics. The energy band gaps are all over 3.85 eV and thermal decomposition temperatures are above 520 ℃.