  We propose the lattice version of $BF$ gravity action whose partition
function leads to the product of a particular form of 15-$j$ symbol which
corresponds to a 4-simplex. The action is explicitly constructed by lattice $B$
field defined on triangles and link variables defined on dual links and is
shown to be invariant under lattice local Lorentz transformation and
Kalb-Ramond gauge transformation. We explicitly show that the partition
function is Pachner move invariant and thus topological. The action includes
the vanishing holonomy constraint which can be interpreted as a gauge fixing
condition. This formulation of lattice $BF$ theory can be generalized into
arbitrary dimensions.
