FinFET devices with epitaxially grown fins and methods for fabricating them are provided. Embodiments include forming at least two shallow trench isolation (STI) regions, filled with dielectric material, adjacent to but separate from each other in a silicon substrate; epitaxially growing a silicon-based layer between each adjacent pair of STI regions to form a fin with a non-rectangular cross-section extending from each STI region to each adjacent STI region; forming a gate oxide over and perpendicular to each fin; and forming a gate electrode over the gate oxide to form a FinFET.