Mid-infrared spectroscopy is a widely used tool for material identification and secondary structure analysis in chemistry, biology and biochemistry. However, the diffraction limit prevents nanoscale protein studies. Here we introduce mapping of protein structure with 30 nm lateral resolution and sensitivity to individual protein complexes by Fourier transform infrared nanospectroscopy (nano-FTIR). We present local broadband spectra of one virus, ferritin complexes, purple membranes and insulin aggregates, which can be interpreted in terms of their α-helical and/or β-sheet structure. Applying nano-FTIR for studying insulin fibrils--a model system widely used in neurodegenerative disease research--we find clear evidence that 3-nm-thin amyloid-like fibrils contain a large amount of α-helical structure. This reveals the surprisingly high level of protein organization in the fibril's periphery, which might explain why fibrils associate. We envision a wide application potential of nano-FTIR, including cellular receptor in vitro mapping and analysis of proteins within quaternary structures.