Strains in GaN nanowires with InGaN quantum wells (QW) were measured from transmission electron microscope (TEM) images. The nanowires, all from a single growth run, are single crystals of the wurtzite structure that grow along the <0001> direction, and are approximately 1000 nm long and 60 nm to 130 nm wide with hexagonal cross-sections. The In concentration in the QWs ranges from 12 to 15 at %, as determined by energy dispersive spectroscopy in both the transmission and scanning electron microscopes. Fourier transform (FT) analyses of <0002> and <1100> lattice images of the QW region show a 4 to 10 % increase of the c-axis lattice spacing, across the full specimen width, and essentially no change in the a-axis value. The magnitude of the changes in the c-axis lattice spacing far exceeds values that would be expected by using a linear Vegard's law for GaN – InN with the measured In concentration. Therefore the increases are considered to represent tensile strains in the <0001> direction. Visual representations of the location and extent of the strained regions were produced by constructing inverse FT (IFT) images from selected regions in the FT covering the range of c-axis lattice parameters in and near the QW. The present strain values for InGaN QW in nanowires are larger than any found in the literature to date for other forms of InxGa1-xN (QW)/GaN.