Abstract We study the Hölder continuity of weak solution u to an equation arising in the stationary motion of electrorheological fluids. To this end, we first obtain higher integrability of Du in our case by establishing a reverse Hölder inequality. Next, based on the result of locally higher integrability of Du and difference quotient argument, we derive a Nikolskii type inequality; then in view of the fractional Sobolev embedding theorem and a bootstrap argument we obtain the main result. Here, the analysis and the existence theory of a weak solution to our equation are similar to the weak solution which has been established in the literature with 3dd+2≤p∞≤p(x)≤p0