A famous theorem of Coburn  says that a nonzero Toeplitz operator  on the Hardy space of the unit diskis injective or its adjoint operator is injective. But the corresponding problem on the Hardy space of the bidisk fails generally. In this talk, we present that certain pluriharmonic symbols or product symbols of one variable functions induce Toeplitz operators satisfying the Coburn type theorem on the Hardy space of the bidisk.