  We show that an action of a supermembrane in an eleven-dimensional spacetime
with a semi-light-cone gauge can be written only with Nambu-Poisson bracket and
an invariant symmetric bilinear form under an approximation. Thus, the action
under the conditions is manifestly covariant under volume preserving
diffeomorphism even when the world-volume metric is flat. Next, we propose two
3-algebraic models of M-theory which are obtained as a second quantization of
an action that is equivalent to the supermembrane action under the
approximation. The second quantization is defined by replacing Nambu-Poisson
bracket with finite-dimensional 3-algebras' brackets. Our models include eleven
matrices corresponding to all the eleven space-time coordinates in M-theory
although they possess not SO(1,10) but SO(1,2) x SO(8) or SO(1,2) x SU(4) x
U(1) covariance. They possess N=1 space-time supersymmetry in eleven dimensions
that consists of 16 kinematical and 16 dynamical ones. We also show that the
SU(4) model with a certain algebra reduces to BFSS matrix theory if DLCQ limit
is taken.
