The evolution of a single dendrite growth and the morphology of multi-dendrite during isothermal solidification of Fe-0.5%C alloy are simulated using phase field method. The effects of supercooling, anisotropy of crystal, interface thickness and crystal orientation as well as the noise on the dendritic morphology are studied. The results illustrate that the morphology of the dendrite is composed of the primary and secondary arms. The process of the dendrite growth and the competition between the dendrite arms are reproduced during solidification. The solute enrichment and the dendrite segregation occur during solidification. The primary arms have the lowest concentration, but the regions between the arms have the highest concentration because of the build-up of solute. With the increment of supercooling, the dendrite grows quickly and the branches are developed. The interface thickness impacts the growth velocity of dendrite. The anisotropy of the crystal exerts an influence on the dendritic morphology. The dendrite grows preferentially when the crystal orientation is consistent with the coordinate axis. The noise leads to the development of the dendritic branches.