In this paper,we use the extended SSH Hamilton model plus Long-range electron correlation Hamiltonian to study change of long-range correlation energy with time in a finite length trans-polyacetylene chain with free boundaries under adiabatic condition in terms of dynamic method.We calculated the effect of the long-rang electron correlation on the polaron dynamics.It is found that the long-rang correlation shows a non-periodic damped oscillation with time when we add an electron or a hole in the trans-polyacetylene chain.After some time,the long-rang correlation energy approaches a constant and at the same time the stable configuration of the lattice is reached.The time that the long-rang correlation energy tends to a constant will decrease with increasing the lattice numbers.