  We present a formulation of a matrix model which manifestly possesses the
general coordinate invariance when we identify the large $N$ matrices with
differential operators. In order to build a matrix model which has the local
Lorentz invariance, we investigate how the $so(9,1)$ Lorentz symmetry and the
$u(N)$ gauge symmetry are mixed together. We first analyze the bosonic part of
the model, and we find that the Einstein gravity is reproduced in the classical
low-energy limit. And we present a proposal to build a matrix model which has
${\cal N}=2$ SUSY and reduces to the type IIB supergravity in the classical
low-energy limit.
