The shape, structure, and orientation of rubbing-aligned cadmium selenide (CdSe) nanorods on polymer coated glass substrates have been studied using transmission electron microscopy (TEM) and grazing incidence X-ray scattering combined with computer simulations. The nanorods are found to be of wurtzite structure and highly monodisperse, and have an essentially ellipsoidal shape with short axes of ~8 nm and long axis of ~22 nm. The nanorods exhibit preferred biaxial orientation with the hexagonal a-c-plane parallel to the sample surface and the c-axis oriented along the rubbing direction of the sample. Some tendency of smectic-A ordering is observed. A quantitative model incorporating atomic structure, rod shape, and preferred orientation was developed for numerically simulating the diffraction peak positions, widths, and intensities, giving good correlation with the experimental observations.