Kirchhoff s law is one of the most fundamental law in thermal radiation. The violation of traditional Kirchhoff s law provides opportunities for higher energy conversion efficiency. Various micro-structures have been proposed to realize single-band nonreciprocal thermal emitters. However, dual-band nonreciprocal thermal emitters remain barely investigated. In this paper, we introduce magneto-optical material into a cascading one-dimensional (1-D) magnetophotonic crystal (MPC) heterostructure composed of two 1-D MPCs and a metal layer. Assisted by the nonreciprocity of the magneto-optical material and the coupling effect of two optical Tamm states (OTSs), a dual-band nonreciprocal lithography-free thermal emitter is achieved. The emitter exhibits strong dual-band nonreciprocal radiation at the wavelengths of 15.337 um and 15.731 um when the external magnetic field is 3 T and the angle of incidence is 56 degree. Besides, the magnetic field distribution is also calculated to confirm that the dual-band nonreciprocal radiation originates from the coupling effect between two OTSs. Our work may pave the way for constructing dual-band and multi-band nonreciprocal thermal emitters.