  Universal speeded-up adiabatic geometric quantum computation~(SAGQC) is
studied in $\Lambda$-type three-level system with different coupling cases,
i.e., time-dependent detuning, large detuning and one-photon resonance
couplings, respectively. In these cases, the counterdiabatic driving method is
used to speed up the universal quantum computation. These schemes in
$\Lambda$-type three-level system are feasible in experiment because additional
unaccessible ground-state-coupling is not needed. Only the shapes and phases of
the initial adiabatic classical-field pulse are modified with the aid of
effective two-level systems based on the counterdiabatic driving. The speed and
robustness against decay of these schemes are discussed and compared. In
addition, our work enriches the study of the speeded-up geometric computation
in $\Lambda$-type three-level system and can be applied to various experimental
platforms with different coupling features.
