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The nonminimal coupling of the kinetic term to Einstein's tensor helps theimplementation of inflationary models due to the gravitationally enhancedfriction. We calculate the parametrized post-Newtonian (PPN) parameters for thescalar--tensor theory of gravity with nonminimally derivative coupling. We findthat under experimental constraint from the orbits of millisecond pulsars inour galaxy, the theory deviates from Einstein's general relativity in the orderof $10^{-20}$, and the effect of the nonminimal coupling is negligible if wetake the scalar field as dynamical dark energy. With the assumed conditionsthat the background scalar field is spatially homogeneous and evolves only oncosmological timescales and the contribution to stress--energy in the solarsystem from the background scalar field is subdominant, the scalar field isrequired to be massless.

PPN parameters in gravitational theory with nonminimally derivative coupling