  Hole-doping effects are investigated on the {\it t-J} ladder model with the
linked-tetrahedra structure. We discuss how a metal-insulator transition occurs
upon hole doping with particular emphasis on the effects of geometrical
frustration. By computing the electron density and the spin correlation
function by the density matrix renormalization group, we show that strong
frustration triggers a first-order transition to a metallic phase, when holes
are doped into the plaquette-singlet phase. By examining spin excitations in a
metallic case in detail, we discuss whether the spin-gap phase persists upon
hole doping according to the strength of frustration. It is further shown that
the lowest excited state in a spin-gap metallic phase can be described in two
independent quasiparticles.
