  We find that quantum spin Hall (QSH) state can be obtained on a square-like
or rectangular lattice, which is generalized from two-dimensional (2D)
transition metal dichalcogenide (TMD) haeckelites. Band inversion is shown to
be controled by hopping parameters and results in Dirac cones with opposite or
same vorticity when spin-orbit coupling (SOC) is not considered. Effective
k$\cdot$p model has been constructed to show the merging or annihilation of
these Dirac cones, supplemented with the intuitive pseudospin texture. Similar
to graphene based honeycomb lattice system, the QSH insulator is driven by SOC,
which opens band gap at the Dirac cones. We employ the center evolution of
hybrid Wannier function from Wilson-loop method, as well as the direct integral
of Berry curvature, to identify the $Z_2$ number. We hope our detailed analysis
will stimulate further efforts in searching for QSH insulators in square or
rectangular lattice, in addition to the graphene based honeycomb lattice.
