Based on the NM/FI/FI/NM double spin filter junction (NM represents the nonmagnetic metal layer and FI the ferromagnetic insulator or semiconductor layer), a new type of double spin filter junction NM/FI/NI/FI/NM (NI represents the nonmagnetic insulator layer) is discussed. By inserting an nonmagnetic insulator layer between the ferromagnetic insulator layers, the adverse influence on the tunneling magnetic resistance (TMR) caused by the magnetic coupling at the interface between the ferromagnetic insulator (FI) layers can be avoided. Using the free-electron approximation and transfer matrix method the dependence of the tunneling conductance and TMR on the thickness of the FI layer and the NI layer and on the bias voltage in the double spin filter junction NM/FI/NI/FI/NM are studied.