  In this paper, we calculate cohomology of a classical Lie algebra of type
$A_2$ over an algebraically field $k$ of characteristic $p=3$ with coefficients
in simple modules. To describe their structure, we will consider them as
modules over an algebraic group $SL_3(k).$ In the case of characteristic $p=3,$
there are only two peculiar simple modules: a simple module isomorphic to the
quotient module of the adjoint module by the center, and a one-dimensional
trivial module. The results on the cohomology of simple nontrivial module are
used for calculate the coomology of the adjoint module. We also calculate
cohomology of the simple quotient algebra Lie of $A_2$ by the center.
