In this paper, a generalized Toeplitz operator is defined and some of results about the classical Toeplitz operator are generalized. In particular, we obtain the necessary and sufficient condition for the product of two such Toeplitz operators to still be Toeplitz operator and the necessary and sufficient condition for such Toeplitz operator to be normal operator. Finally, a necessary condition for two such Toeplitz operators to be commutative is established.
