  Recently, Belle Collaboration reported a new exotic state $Y(4620)$ with mass
at 4625.9 MeV in the positronium annihilation process. Inspired by experiment,
we study the tetraquark system $c\bar{s}s\bar{c}$ with quantum numbers
$J^{P}=1^{-}$ in the framework of chiral constituent quark model with the help
of Gaussian expansion method. Two structures, diquark-antidiquark and
meson-meson, with all possible color and spin configurations are considered.
The result shows that no bound state can be formed. To investigate the possible
resonance states, the real scaling method is employed. Several resonance states
with energies 4354, 4408, 4469, 4497 and 4531 MeV, are proposed. Taking into
account the errors in calculating the $q\bar{q}$ mesons, the system errors in
the calculation of four-quark system are around 60$\sim 100$ MeV. The resonance
with energy 4531 MeV is possible the candidate of the newly found state
$Y(4620)$.
