The molecular mechanism of epitaxial fibril formation has been investigated for GAV-9 (NH3+-VGGAV-VAGV-CONH2), an amyloid-like peptide extracted from a consensus sequence of amyloidogenic proteins, which assembles with very different morphologies, "upright" on mica and "flat" on the highly oriented pyrolytic graphite (HOPG). Our all-atom molecular dynamics simulations reveal that the strong electrostatic interaction induces the "upright" conformation on mica, whereas the hydrophobic interaction favors the "flat" conformation on HOPG. We also show that the epitaxial pattern on mica is ensured by the lattice matching between the anisotropic binding sites of the basal substrate and the molecular dimension of GAV-9, accompanied with a long-range order of well-defined beta-strands. Furthermore, the binding free energy surfaces indicate that the longitudinal assembly growth is predominantly driven by the hydrophobic interaction along the longer crystallographic unit cell direction of mica. These findings provide a molecular basis for the surface-assisted molecular assembly, which might also be useful for the design of de novo nanodevices.