We point out that the pseudogap phenomena observed in under-doped high-T-c, cuprates are naturally understood as a precursor of the strong coupling superconductivity and this idea does not contradict with their magnetic field dependences. The strong coupling superconductivity necessarily leads to the strong fluctuations with a character of the pre-formed pairs. The pre-formed pairs have small dispersion and are thermally excited in the vicinity of the critical point. The gap structures of the spectral weight and the density of states result from such strong fluctuations and give rise to the reduction of the NMR spin-lattice relaxation rate in the wide temperature region. On the basis of this idea, the magnetic field dependence of the pseudogap phenomena is naturally shown to be remarkably small in the strong coupling case. These features well explain the experiments. (C) 2000 Elsevier Science B.V. All rights reserved.