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High-entropy alloys (HEAs) consist of five or more metallic elements in equal or near-atomic proportions to form multicomponent alloys with high configurational entropy. Recently, nanostructured HEAs have attracted considerable attention from both academia and industry for their extraordinary properties. Nucleation during solidification directly affects the properties of metals and alloys. Although experimental techniques to study the microstructure and nucleation growth during metal solidification continue to make remarkable developments, many unanswered questions remain in this field. Molecular dynamics (MD) simulation is an effective tool to describe the nucleation mechanism and microstructural evolution of HEAs during solidification processes. In this paper, we explore the atomic origins of the homogeneous and heterogeneous nucleation in the FeNiCrCoCu HEA using classical MD simulations. The results show an obvious difference between homogeneous and heterogeneous nucleation. A new growth pattern of crystals in HEA was discovered during the heterogeneous nucleation process. The mechanisms of heterogeneous and homogeneous nucleation and their control factors are revealed through the evolution of several crystalline structures and dislocation density.