  In this paper we study the Generalized Minimal Massive Gravity (GMMG) in
asymptotically $AdS_3$ background. The generalized minimal massive gravity
theory is realized by adding the CS deformation term, the higher derivative
deformation term, and an extra term to pure Einstein gravity with a negative
cosmological constant. We study the linearized excitations around the $AdS_3$
background and find that at special point (tricritical) in parameter space the
two massive graviton solutions become massless and they are replaced by two
solutions with logarithmic and logarithmic-squared boundary behavior. So it is
natural to proposed that GMMG model could also provide a holographic
description for a $3-$rank Logarithmic Conformal Field Theory (LCFT). We
calculate the energy of the linearized gravitons in $AdS_3$ background, and
show that the theory is free of negative-energy bulk modes. Then we obtain the
central charges of the CFT dual explicitly and show GMMG also avoids the
aforementioned "bulk-boundary unitarity clash". After that we show that General
Zwei-Dreibein Gravity (GZDG) model can reduce to GMMG model. Finally by a
Hamiltonian analysis we show that the GMMG model has no Boulware-Deser ghosts
and this model propagate only two physical modes.
