  The definitions of the quark and gluon transversity generalized parton
distributions (GPDs) in spin-3/2 particles are obtained in the light-cone
gauge. It is found that they contain 16 independent components for each parton.
Their even or odd property is found in terms of skewness variable, and the odd
transversity GPDs vanish in the forward limit. There are 16 amplitudes with
helicity flip of quark or gluon. We conclude that all the amplitudes,
unpolarized, polarized, and transversity amplitudes, have a common factor
$F(\zeta)$ carrying all the complex part. Here, the variable $\zeta$ is the
helicity difference $\zeta=(\lambda' -\lambda)-(\mu' - \mu)$ for the amplitude
$\mathcal{A}_{\lambda' \mu',\lambda\mu}$. This kinematical factor is associated
with the transfer of the orbital angular momentum in the quark- and
gluon-spin-3/2 particle scattering amplitudes. We also derive another main
physical quantity, transversity distribution, from the transversity GPDs in the
forward limit for the spin-3/2 particles.
