Martin expression about the quantum defect of single-valence atoms is extended to many-valence atoms by identifying the weakest bound electron (WBE) under the weakest bound electron potential model (WBEPM) theory. Six Rydberg series energy levels of 2p6np2Po_(1/2) (n>3), 2p6np2Po_(3/2) (n>3), 2p6nd2D_(3/2) (n>3), 2p6nd2D_(5/2) (n>3), 2p6nf2Fo_(5/2) (n>4), and 2p6nf2Fo_(7/2) (n>4) for Ni XVIII are calculated by this method. The calculated results are in good agreement with the experimental results.