Marangoni instability in well-defined non-spherical sessile droplet of 0.65cSt silicone oil evaporating at constant contact line mode is investigated through a series of experiments. Droplets of typical regular geometries (such as triangular, square, pentagonal and elliptical) and exotic shapes (such as kidney and positive-positive curvature) are tested. Cell patterns of Benard-Marangoni instability are distributed along the azimuthal direction non-uniformly in the droplets. These cells always occur first at the region where the curvature of the three-phase contact line (k(cl)) is the largest and they do not fill the whole droplet at once. Different from that in spherical droplet, there is no such a steady state in the non-spherical droplets and these BM cells always drift from the lower k(cl) regions towards the higher ones. The influences of k(cl), the substrate temperature and the contact angle on the patterns of the Benard-Marangoni instability are analyzed. The critical contact angles for the onset of Marangoni instability are determined. (C) 2019 Elsevier Ltd. All rights reserved.