  Recently LHCb declared a new structure $X(6900)$ in the final state
di-$J/\psi$ which is popularly regarded as a $cc$-$\bar c\bar c$ tetraquark
state. %popularly. Within the Bethe-Salpeter (B-S) frame we study the possible
$cc$-$\bar c\bar c$ bound states and the interaction between diquark ($cc$) and
antidiquark ($\bar c\bar c$). In this work $cc$ ($\bar c\bar c$) is treated as
a color anti-triplet (triplet) axial-vector so the quantum numbers of
$cc$-$\bar c\bar c$ bound state are $0^+$, $1^+$ and $2^+$. Learning from the
interaction in meson case and using the effective coupling we suggest the
interaction kernel for diquark and antidiquark system. Then we deduce the B-S
equations for different quantum numbers. Solving these equations numerically we
find the spectra of some excited states can be close to the mass of $X(6900)$
when we assign appropriate values for parameter $\kappa$ introduced in the
interaction (kernel).We also briefly calculate the spectra of $bb$-$\bar b\bar
b$ bound states. Future measurement of $bb$-$\bar b\bar b$ state will help us
to determine the exact form of effective interaction.
