The bright long gamma-ray burst GRB 141207A was observed by the {it Fermi Gamma-ray Space Telescope} and detected by both instruments onboard. The observations show that the spectrum in the prompt phase is not well described by the canonical empirical Band function alone, and that an additional power-law component is needed. In the early phase of the prompt emission, a modified blackbody with a hard low-energy photon index ($alpha$ = +0.2 -- +0.4) is detected, which suggests a photospheric origin. In a finely time-resolved analysis, the spectra are also well fitted by the modified blackbody combined with a power-law function. We discuss the physical parameters of the photosphere such as the bulk Lorentz factor of the relativistic flow and the radius. We also discuss the physical origin of the extra power-law component observed during the prompt phase in the context of different models such as leptonic and hadronic scenarios in the internal shock regime and synchrotron emission in the external forward shock. In the afterglow phase, the temporal and spectral behaviors of the temporally extended high-energy emission and the fading X-ray emission detected by XRT on-board {it Swift} are consistent with synchrotron emission in a radiative external forward shock.