  We construct a generalized massive gravity by combining quadratic curvature
gravity with the Chern-Simons term in four dimensions. This may be a candidate
for the parity-odd tricritical gravity theory. Considering the AdS$_4$ vacuum
solution, we derive the linearized Einstein equation, which is not similar to
that of the three dimensional (3D) generalized massive gravity. When a
perturbed metric tensor is chosen to be the Kerr-Schild form, the linearized
equation reduces to a single massive scalar equation. At the tricritical points
where two masses are equal to -1 and 2, we obtain a log-square wave solution to
the massive scalar equation. This is compared to the 3D tricritical generalized
massive gravity whose dual is a rank-3 logarithmic conformal field theory.
