A complex directional element adapting to wide area backup protection system is proposed. Firstly，the operation characteristics of positive-sequence fault component directional element and negative-sequence directional element are analyzed. Then a virtual variable quantity directional element is presented to cope with the drawbacks of the above elements. By creating virtual voltage and current，the virtual variable quantity directional element will produce the virtual variable quantities of voltage and current when a symmetrical fault occurs，which can be used to identify the fault direction persistently. Based on the three kinds of elements，the composition logic of the complex directional element is put forward. Finally，the simulation results demonstrate that the complex directional element can start reliably，operate accurately and keep effectiveness constantly to all kinds of short-circuit faults. And other advantages include no dead zone with a three-phase fault close to the element，high sensitivity with a strong source behind the element，and automatic return after external faults disappeared. Therefore，the complex directional element has a good performance to meet the requirement of wide area backup protection.