To violate Kirchhoff’s law is very important in the areas of thermal radiation. However, due to the weak nonreciprocity in natural materials, it is necessary to engineer novel structures to break the balance between emission and absorption. In this work, we introduce magneto-optical material into Fibonacci photonic crystals. Assisted by the nonreciprocity of the magneto-optical material and the excitation of Tamm plasmon polaritons, strong nonreciprocal thermal radiation can be realized. The difference between absorption and emission at wavelength of 16 μm can reach 0.9 at the incident angle of 60o. The distributions of the magnetic field are also calculated to verify the underlying physical origin. By engineering the parameters of the structure, it is found that strong nonreciprocal thermal radiation can be achieved at shorter wavelength and smaller incident angle. The results indicate that the Fibonacci magnetophotonic crystals are the promising candidate to engineer the nonreciprocal emission for various requirements.