In this paper, we discuss the disjoint hypercyclicity of linear composition on the weighted Banach spaces.Moreover,according to the difference of the analytic maps,we obtain a sufficient condition for the disjoint hypercyclicity and disjoint supercyclicity of composition operators on $H^\infty_{\alpha,0}$. Moreover,we also obtain a partial characterization for the hypercyclicity of weighted composition operators on $H^\infty_{\alpha,0}$.
