  We investigate quantum deformation of conformal algebras by constructing the
quantum space for $sl_q(4,C)$. The differential calculus on the quantum space
and the action of the quantum generators are studied. We derive deformed
$su(4)$ and $su(2,2)$ algebras from the deformed $sl(4)$ algebra using the
quantum 4-spinor and its conjugate spinor. The 6-vector in $so_q(4,2)$ is
constructed as a tensor product of two sets of 4-spinors. The reality condition
for the 6-vector and that for the generators are found. The q-deformed
Poincar{\'e} algebra is extracted as a closed subalgebra.
