  We study bosonic closed string scattering amplitudes in the high-energy
limit. We find that the methods of decoupling of high-energy zero-norm states
and the high-energy Virasoro constraints, which were adopted in the previous
works to calculate the ratios among high-energy open string scattering
amplitudes of different string states, persist for the case of closed string.
However, we clarify the previous saddle-point calculation for high-energy open
string scattering amplitudes and claim that only (t,u) channel of the
amplitudes is suitable for saddle-point calculation. We then discuss three
evidences to show that saddle-point calculation for high-energy closed string
scattering amplitudes is not reliable. By using the relation of tree-level
closed and open string scattering amplitudes of Kawai, Lewellen and Tye (KLT),
we calculate the high-energy closed string scattering amplitudes for arbitrary
mass levels. For the case of high-energy closed string four-tachyon amplitude,
our result differs from the previous one of Gross and Mende, which is NOT
consistent with KLT formula, by an oscillating factor.
