  We study the spin-orbital interaction and the spin Hall effect(SHE) of an
electron moving on a noncommutative space under the influence of a vector
potential A. On a noncommutative space we find that the commutator between the
vector potential A and the electric potential V_1(r) of lattice induces a new
term which can be treated as an effective electric field, and the spin-Hall
conductivity obtains some correction. In addition, the spin current as well as
spin-Hall conductivity have distinct values in different direction. On a
noncommutative space we derive the spin-depended electric current whose
expectation value gives the spin Hall effect and spin Hall conductivity. We
have defined a new parameter \varsigma=\rho\theta (\rho is electron
concentration, \theta is noncommutative parameter) which can be measured
experimentally. Our approach is based on the Foldy-Wouthuysen transformation
which give a general Hamiltonian of a non-relativistic electron moving on a
noncommutative space.
