(X=Zn, Cd; Y=As, Sb)*

Based on first-principles calculations and effective k.p model analysis, we have studied three Zintl compounds, including Ba₃Zn₂As₄, Ba₃Cd₂As₄ and Ba₃Cd₂Sb₄, to reveal their electronic band topology under different conditions, such as including and not including spin-orbit coupling (SOC) and different external strains. We find that these family materials are close to the boundaries of several topological phases. When SOC is ignored, there are topological nodal lines around Fermi energy due to band inversion between valence and conduction bands at one or two time-reversal invariant momenta, which can be tuned by proper strain. When SOC is further included, these nodal lines are gaped and these materials become weak or strong topological insulators (TIs). They are suitable for studying topological phase transition.