Perovskite epitaxial multiferroic BiFeO3 nanoislands were grown on SrTiO3 (100) and Nb-doped SrTiO3 (100) single crystal substrates by chemical self-assembled method. Their phase structure and morphology were characterized by X-ray diffraction, scanning electron microscopy, and atomic force microscopy, respectively. The results showed that epitaxial multiferroic BiFeO3 nanoislands were obtained via post-annealing process in the temperature range of 650 - 800°C, and their lateral sizes were in the range of 50 - 160 nm and height of 6 -12 nm. With increasing the post-annealing temperature, the morphology of BiFeO3 nanoisland in the (100) growth plane evolved from tri-angled to squared, and then to plated shapes. By using piezo-force microscopy, ferroelectric characteristics of a single epitaxial BiFeO3 nanoisland (with lateral size of ~ 50 nm and height of 12 nm) grown on Nb-doped SrTiO3 (100) single crystal substrate, was characterized. The results demonstrated that fractal ferroelectric domains existed in the single BiFeO3 nanoisland, and self-biased polarization was also observed within this multiferroic nanoisland. This phenomenon can be ascribed to the interfacial stress caused by the lattice misfit between the BiFeO3 nanoisland and the SrTiO3 single crystal substrate.