Structural evolution and thermal stability of nanoclusters supported on the substrate play a key role in their applications. In this paper, we study the melting of the mixed Co281Cu280 bimetallic cluster with the icosahedral configuration by using molecular dynamics simulation with a general embedded atom method. The influence of the free or fixed Cu(010) substrate on the melting of the supported cluster is explored. It is found that the melting is strongly related to the substrate condition. There is a sharp increase in the temperature-energy curve for the cluster on the free substrate. The melting point (1320 K) is much lower than that (1630 K) of the cluster on the fixed substrate. The icosahedral configuration is converted into epitaxial cluster along the (010) of the substrate. Premelting occurs for the epitaxial cluster with the increase of temperature. The premelted atoms diffuse to the surface of the substrate and form surface layer until the cluster melt. The variation of the atomic spreading for the cluster on the free substrate is different from the case on the fixed substrate due to the atomic embedding into the substrate.