  In this paper we study a model of s-wave marginal Fermi liquid superconductor
at two dimensions. Besides the usual Bardeen-Cooper-Schrieffer(BCS) point
attractive interaction, the fermions in our system also interact {\em via} a
long range repulsive interaction $v(q)=g_{D}/q^2$. We find that although
superconductivity is not destroyed by the long-ranged repulsion interaction
(demonstrated by the existence of Meissner effect), nevertheless the BCS
pairing function $\Delta_{BCS}$ is strongly suppressed resulting in power-law
correlation $<\Delta_{BCS}(\vec{x})\Delta_{BCS}(0)>\sim|\vec{x}|^{-2\gamma}$.
This observation is explained within a general picture of marginal Fermi
liquid.
