We investigate whether interaction between massive neutrinos and quintessence scalar field is the origin of the late time accelerated expansion of the universe . We present cosmological perturbation theory in neutrinos probe interacting dark-energy models , and calculate cosmic microwave background anisotropies and matter power spectrum . In these models , the evolution of the mass of neutrinos is determined by the quintessence scalar field , which is responsible for the cosmic acceleration today . We consider several types of scalar field potentials and put constraints on the coupling parameter between neutrinos and dark energy . Assuming the flatness of the universe , the constraint we can derive from the current observation is \sum m _ { \nu } < 0.87 eV at the 95 \% confidence level for the sum over three species of neutrinos . We also discuss on the stability issue of the our model and on the impact of the scattering term in Boltzmann equation from the mass-varying neutrinos .