  We study a nonminimal derivative coupling (NMDC) of scalar field, where the
scalar field is coupled to curvature tensor in the five dimensional universal
extra dimension model. We apply the Einstein equation and find its solution.
First, we consider a special case of pure free scalar field without NMDC and we
find that for static extradimension, the solution is equivalent to the standard
cosmology with stiff matter. For a general case of pure free scalar field with
NMDC, we find that the de Sitter solution is the solution of our model. For
this solution, the scalar field evolves linearly in time. In the limit of small
Hubble parameter, the general case give us the same solution as in the pure
free scalar field. Finally, we perform a dynamical analysis to determine the
stability of our model. We find that the extradimension, if it exist, can not
be static and always shrinks with the expansion of four dimensional spacetime.
