Recently, the rare-earth monopnictide compounds LnPn have attracted considerable attention in condensed matter physics studies due to their possible topological properties. We have performed systematic first principles study of the electronic structure and band topology properties of LnPn (Ln=Ce, Pr, Sm, Gd, Yb; Pn=Sb, Bi). Assuming the f-electrons are well localized in these materials, both hybrid functional and modified Becke-Johnson calculations yield electronic structure in good agreement with experimental observations, while generalized gradient approximation calculations severely overestimate the band inversions. From Ce to Yb, a systematic reduction of band inversion with respect to the increasing Ln atomic number is observed, and Z2 for CePn and YbPn are [1;000] and [0;000], respectively. In both hybrid functional and modified Becke-Johns calculations, a topologically non-trivial to trivial transition is expected around SmSb for the antimonides and around DyBi for the bismuthides. Such variation is related with lanthanide contraction, but is different from simple pressure effects.