Abstract: The Cauchy problem for a dynamical Q-tensor model which couples a forced Navier-Stokes equations with a parabolic-type Q-tensor system in three-dimensional space is considered. Firstly, the global existence of weak solutions is proved by energy method and classical Friedrich's method, and the higher regularity of the global weak solutions is estimated provided that the viscosity of the fluid is sufficiently large. Then, the global existence of strong solutions is established.Finally, a continuous dependence result on the initial data is also given.