  We investigate cosmological behavior in the quasi-Dilaton non-linear massive
gravity. We perform a detailed dynamical analysis and examine the stable
late-time solutions relevant to late time cosmic acceleration. We demonstrate
that a dark-energy dominated, cosmological-constant-like solution is a late
attractor of the dynamics. We also analyze the evolution of the universe at
intermediate times, showing that the observed epoch sequence can be easily
obtained in the model under consideration. Furthermore, we study the
non-singular bounce and the cosmological turnaround which can be realized for a
region of the parameter space. Last but not least, we use observational data
from Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations (BAO) and Cosmic
Microwave Background (CMB), in order to constrain the parameters of the theory.
