The unsteady 2D flow of a generalized Newtonian fluid is considered. The velocity \(v(x,t)=(v_1,v_2)\) and the pressure \(p(x,t)\) satisfy to the equations \[ \begin{aligned} &\frac{\partial v}{\partial t}+(v\cdot\nabla)v-\text{div}\,\sigma(v)+\nabla p=f,\quad\text{div}\,v=0, \quad x\in\Omega,\quad t\in (0,T),\\ &v(x,0)=v_0(x),\quad x\in \Omega,\\ &v(x,t)=0, \quad x\in\partial\Omega,\quad t\in (0,T).\end{aligned} \] Here \(\Omega\subset \mathbb R^2\) is a bounded domain with smooth boundary, \(\sigma(v)\) is a stress tensor of a form \[ \sigma(v)=2\mu(| S| ^2)S,\quad S(v)=\nabla v+(\nabla v)^T, \] where \(\mu\) is a given function such that the tensor \(\sigma(v)\) has the growth of order \(q-1\) for a certain \(q\in [2,4)\). The typical example of \(\sigma(v)\) is \[ \sigma(v)=\left(1+| S| ^2\right)^{\frac{q-2}{2}}S. \] It is proved that the unique weak solution to the problem has a Hölder continuous gradient if the data \(f\) and \(v_0\) are sufficiently smooth.