Illumination for line-scan machine vision systems is required to produce a highly asymmetric elliptical beam pattern, to maximize system speed and accuracy. The use of LED emitters with symmetric Lambertian emission patterns is challenging in this context, requiring significant beam reshaping. A design for a collimated line-light, with long working distance, utilizing LEDs with symmetric Lambertian emission patterns, is presented. Using a combination of Fresnel lenses and total internal reflection (TIR) optics, an elliptical beam with a high degree of collimation is achieved. TIR elements are designed based on an adaptation of a freeform lens design method published by Chen et al. [Opt. Express 20, 10 (2012)]. Practical performance of the design is verified experimentally using a prototype unit. In addition, the design is compared, using ray tracing software, to line-lights constructed using commercially available symmetric and elliptical TIR lenses, and its superior performance is confirmed. The optical design described is fully manufacturable and suitable for both smalland large-scale production.