  We propose a method of multi-regulator functional renormalization group
(MR-FRG) which is a novel formulation of functional renormalization group with
multiple infrared regulators. It is applied to a two-component fermionic system
with an attractive contact interaction to study crossover phenomena between the
Bardeen-Cooper-Schrieffer (BCS) phase and the Bose-Einstein condensation (BEC)
phase. To control both the fermionic one-particle excitations and the bosonic
collective excitations,IR regulators are introduced, one for the fermionic
two-point function and another for the four-fermion vertex. It is shown that
the Nozi\`eres-Schmitt-Rink (NSR) theory, which is successful to capture
qualitative features of the BCS-BEC crossover, can be derived from MR-FRG. Some
aspects of MR-FRG to go beyond the NSR theory are also discussed.
