  Six dimensional compactification of the type IIA matrix model on the ${\bf
Z}$-orbifold is studied. Introducing a ${\bf Z}_{3}$ symmetry properly on the
three mirror images of fields in the $N$-body system of the supersymmetric D0
particles, the action of the Matrix model compactified on the ${\bf
Z}$-orbifold is obtained. In this matrix model ${\cal N}=1$ supersymmetry is
explicitly demonstrated.
