  An analytical formula of the production cross section for $e^+ e^-$
annihilates to hadrons considering the initial state radiation is reported in
the paper. Comparisons between the analytical formula and the direct
integration of ISR shows good accuracy which satisfy the current experimental
requirements. Besides, comparison in the cross section between the analytical
formula and the calculation with ConExc Monte Carlo generator is also
presented. The analytical formula greatly shorten the computing time which
could be used for fitting procedure to extract the parameters of narrow
charmonium resonances.
