  We develop a Fermionic Chern-Simons (CS) theory for the fractional quantum
Hall effect in monolayer graphene with SU(4) symmetry, arising from the spin
and the valley degrees of freedom, which involves four distinct CS gauge
fields. We choose the corresponding elements of the CS coupling matrix such
that an even number of spin and valley quantum number dependent flux quanta is
attached to all electrons and that any electron with a given spin and valley
quantum number sees an integer number of flux attached to other electrons with
different (spin and valley) quantum numbers. Using this CS matrix, we obtain a
list of possible fractional quantum Hall states that might occur in graphene
and propose wavefunctions for those states. Our analysis also applies to
fractional quantum Hall states of both bilayer quantum Hall systems without
spin polarization and bilayer spin polarized graphene.
