Considering a three-dimensional C−metric, we obtain the exact accelerating black holes in the F(R) theory of gravity coupled with and without a matter field. First, we extract uncharged accelerating AdS black hole solutions in F(R) gravity. Then, we study the effects of various parameters on metric function, roots, and the temperature of these black holes. The temperature is always positive for the radii less than 1 α , and it is negative for the radii more than 1 α . We extend our study by coupling nonlinear electrodynamics as a matter filed to F(R) gravity to obtain charged black holes in this theory. Next, we evaluate the effects of different parameters such as the electrical charge, accelerating parameter, angular, F(R) gravity, and scalar curvature on the obtained solutions, roots, and temperature of three-dimensional charged accelerating AdS black holes. The results indicate that there is a root in which it depends on various parameters. The temperature of these black holes is positive after this root.
