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. A strong coupling superconductivity necessarily leads to strong fluctuations. In particular, the superconducting fluctuations, which are strongly diffusive within the conventional weak coupling theory, become propagative and have a character of the pre-formed pairs in the strong coupling case. Such strong fluctuations lead to the gap structure of both the spectral weight and the density of states. The superconducting critical temperature is strongly reduced by the fluctuations in the strong coupling case. (C) 2000 Published by Elsevier Science B.V. All rights reserved.