  We investigate non-commutative differential calculus on the supersymmetric
version of quantum space where the non-commuting super-coordinates consist of
bosonic as well as fermionic (Grassmann) coordinates. Multi-parametric quantum
deformation of the general linear supergroup, $GL_q(m|n)$, is studied and the
explicit form for the ${\hat R}$-matrix, which is the solution of the
Yang-Baxter equation, is presented. We derive the quantum-matrix commutation
relation of $GL_q(m|n)$ and the quantum superdeterminant. We apply these
results for the $GL_q(m|n)$ to the deformed phase-space of supercoordinates and
their momenta, from which we construct the ${\hat R}$-matrix of q-deformed
orthosymplectic group $OSp_q(2n|2m)$ and calculate its ${\hat R}$-matrix. Some
detailed argument for quantum super-Clifford algebras and the explict
expression of the ${\hat R}$-matrix will be presented for the case of
$OSp_q(2|2)$.
