  On the basis of the Berkovits pure spinor formalism of covariant quantization
of supermembrane, we attempt to construct a M(atrix) theory which is covariant
under $SO(1,10)$ Lorentz group. We first construct a bosonic M(atrix) theory by
starting with the first-order formalism of bosonic membrane, which precisely
gives us a bosonic sector of M(atrix) theory by BFSS. Next we generalize this
method to the construction of M(atrix) theory of supermembranes. However, it
seems to be difficult to obtain a covariant and supersymmetric M(atrix) theory
from the Berkovits pure spinor formalism of supermembrane because of the matrix
character of the BRST symmetry. Instead, in this paper, we construct a
supersymmetric and covariant matrix model of 11D superparticle, which
corresponds to a particle limit of covariant M(atrix) theory. By an explicit
calculation, we show that the one-loop effective potential is trivial, thereby
implying that this matrix model is a free theory at least at the one-loop
level.
