A novel equiatomic Ni20Ti20Fe20Al20Cu20 high-entropy alloy was designed and fabricated in order to investigate plastic deformation mechanisms at high temperatures. Plenty of nano-precipitates are able to be observed in the as-cast high-entropy alloy. The nano-precipitate belongs to a face-centered cubic (FCC) structure, while the matrix possesses a body-centered cubic (BCC) structure. The high-entropy alloy exhibits the poor plasticity at room temperature, but it exhibits the high plasticity at elevated temperatures. The nano-precipitates gradually grow with the increase in the deformation temperature at elevated temperatures, where there exists an orientation relationship of [011](FCC)//[011](BCC) between the precipitate and the matrix. The plastic flow stress of Ni20Ti20Fe20Al20Cu20 high-entropy alloy at elevated temperatures is characterized by a steady state, which can be attributed to a competition between the increase of dislocation density due to plastic strain and the decrease of dislocation density due to dynamic recrystallization. In the case of elevated temperatures, plastic deformation mechanism for dislocation slip occurs in the matrix of Ni20Ti20Fe20Al20Cu20 high-entropy alloy, while plastic deformation mechanism for deformation twinning is dominant in the precipitates. Therefore, dislocation slip and deformation twinning play a significant role in plastic deformation of Ni20Ti20Fe20Al20Cu20 high-entropy alloy at elevated temperatures.