  In this paper, we investigate the influence of gravity and noncommutativity
on Dirac equation. By adopting the tetrad formalism, we show that the modified
Dirac equation keeps the same form. The only modification is in the expression
of the covariant derivative. The new form of this derivative is the product of
its counterpart given in curved space-time with an operator which depends on
the noncommutative $\theta$-parameter. As an application, we have computed the
density number of the created particles in presence of constant strong electric
field in an anisotropic Bianchi universe.
