  A Lorentz covariant matrix regularization of membrane thories is studied.It
is shown that the action for a bosonic membrane can be defined by matrix
regularization in a Lorentz covariant manner. The generator of area preserving
diffeomorphism can also be consistently defined by matrix regularization, and
we can make the area preserving gauge symmetry manifest. However, the
reparametrization BRST charge explicitly depends on a specific basis set
introduced to define the matrix regularization. We also briefly comment on an
extension of the present formulation to a supermembrane.
