The nonlocal effect on the spontaneous emission of a silver cuboid dimer is investigated using a local analog model. Magnetic as well as electric dipole excitations are introduced to excite different gap modes. The nonlocal response of electric and magnetic modes on various parameters of gap (width and refractive index) are investigated. Unidirectional radiation is achieved by the interaction between electric and magnetic modes in both local and nonlocal models. Compared to local simulations, the resonant wavelength is blue shifted and the spontaneous emission enhancement is weakened in the nonlocal model. The relative shifts of the resonant wavelengths get larger in smaller gaps with a higher refractive index.