A nonlinear optical effect of a second harmonic generation (SHG) was first observed in quartz and then found in many inorganic materials that have an asymmetric crystalline structure. Second-order nonlinear responses were also found in organic and biomaterials and are exploited for fundamental studies of helical and chiral biological molecules, such as proteins and amyloid fibrils. Another class of biomaterials is man-made bioinspired nanostructures, which are composed of chemically synthesized biomolecules and are self-assembled into supramolecular nanofibrils. Most of these materials have an asymmetric crystalline structure and possess ferroelectric and related phenomena. Here, the SHG effect is studied in bio-organic peptide nanostructures of different morphologies and symmetries. These nanostructures are self-assembled in different solvents from peptide precursors with a variable number of phenylalanine (F) amino acid units. A pronounced SHG response is detected in FFF-nanobelts, FF-nanotubes, and FFF-nanospheres. SHG and Raman spectroscopy studies during phase transformation in FF-nanotubes allow the definition of the intermolecular bonds responsible for SHG. Using two-photon optical microscopy, orientational molecular ordering in aligned peptide supramolecular structures is found by adapting a generic model developed earlier for diverse biological protein fibrils. Efficient optical frequency conversion from NIR to green and blue light is demonstrated, as well as an effect of nonlinear optical waveguiding. These results suggest these bioinspired nanostructures as promising for a new generation of nonlinear optical nanomaterias, which can be integrated into nanophotonic devices.