This paper investigated H-Toeplitz operators on the bidisk Bergman space $L_a^2({\mathbb{D}}^2)$. First, we provided the matrix-type representation for the H-Toeplitz operator $B_{\varphi }$. Next, we presented the necessary and sufficient conditions for such operators to be co-isometries and partial isometries. Then, we proved that any diagonal H-Toeplitz operator with some pluriharmonic symbol must be the zero operator. Finally, we characterized several invariant subspaces and kernel spaces associated with H-Toeplitz operators.