  In this paper, it is proved that the infinite KAM torus with prescribed
frequency exists in a sufficiently small neighborhood of a given $ I^{0}$ for
nearly integrable and analytic Hamiltonian system $ H(I,\theta) = H_{0}(I)+
\epsilon H_{1}(I,\theta)$ of infinite degree of freedom and of short range.
That is to say, we will give an extension of the original Kolmogorov theorem to
the infinite-dimensional case of short range. The proof is based on the
approximation of finite-dimensional Kolmogorov theorem and an improved KAM
machinery which works for the normal form depending on initial $ I^{0}$.
