‎In this paper‎, ‎we study character amenability of semigroup algebras `ell^{1}(S)` and weighted semigroup algebras $ ell^{1} (S,omega)$‎, ‎for a certain semigroups such as right(left) zero semigroup‎, ‎rectangular band semigroup‎, ‎band semigroup and uniformly locally finite inverse semigroup‎. ‎In particular‎, ‎we show that for a right (left) zero semigroup or a rectangular band semigroup‎, ‎character amenability‎, ‎amenability‎, ‎pseudo‎ - ‎amenability of $ ell^{1} (S,omega)$‎, ‎for each weight $ omega $‎, ‎are equivalent‎. ‎We also show that for an archimedean semigroup $ S $‎, ‎character pseudo‎ - ‎amenability‎, ‎amenability‎, ‎approximate amenability and pseudo-amenable of $ ell^{1}(S) $ are equivalent‎.