This paper characterizes the hypercyclicity of weighted composition operators on the H_v⁰ space. The sufficient condition of hypercyclicity of weighted composition operators is presented, when φ is an automorphism or a hyperbolic non-automorphisms. The examples showing the fact that weighted composition operators uC_φ on the H_v⁰ space are non-hypercyclic are also given, when φ is parabolic nonautomorphisms.