  We construct spherically symmetric and static solutions in $F(R)$ gravity
coupled with electromagnetic fields. The solutions include new types of black
holes with electric and magnetic charges. We show that the higher-derivative
terms make the curvature singularity much softer than that in the charged black
holes in Einstein's general relativity. We calculate some thermodynamical
quantities of the obtained black holes like entropy, Hawking radiation, and
quasi-local energy and we confirm that the black hole solutions satisfy the
first law of thermodynamics. Finally, we study the stability analysis using the
odd-type mode and show that there are stable black hole solutions and the
radial speed of the parity-odd mode is unit, that is, the speed of light.
