In this Letter, we consider the theory of F(R) gravity with the Lagrangian density £=R+αR2+βR2lnβR£=R+αR2+βR2lnβR. We obtain the constant curvature solutions and find the scalar potential of the gravitational field. We also obtain the mass squared of a scalaron in the Einstein's frame. We find cosmological parameters corresponding to the recent Plank 2015 results. Finally, we analyze the critical points and stability of the new modified theory of gravity and find that logarithmic correction is necessary to have successful model.
