Nuclear magnetic resonance (NMR) measurements of an iron (Fe)-based superconductor LaFeAsO_{1-x}F_x (x = 0.08 and 0.14) were performed at ambient pressure and under pressure. The relaxation rate 1/T_1 for the overdoped samples (x = 0.14) shows T-linear behavior just above T_c, and pressure application enhances 1/T_1T similar to the behavior of T_c. This implies that 1/T_1T = constant originates from the Korringa relation, and an increase in the density of states at the Fermi energy D(E_F) leads to the enhancement of T_c. In the underdoped samples (x = 0.08), 1/T_1T measured at ambient pressure also shows T-independent behavior in a wide temperature range above T_c. However, it shows Curie-Weiss-like T dependence at 3.0 GPa accompanied by a small increase in T_c, suggesting that predominant antiferromagnetic fluctuation suppresses development of superconductivity or remarkable enhancement of T_c. The qualitatively different features between underdoped and overdoped samples are systematically explained by a band calculation with hole and electron pockets.
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