In this paper the problem of path following or trajectory tracking by an unmanned aerial vehicle (UAV) is considered. Several guidance laws have been presented in literature to this end. Among them, L1 guidance strategy, which has similarity with proportional navigation guidance, has received most attention. However, the constant value of look-ahead distance L1 considered in that guidance algorithm poses a drawback that leads to degraded performance in path following for varied range of radius of curvature of paths. To obviate this drawback, this paper presents a variable L1 path-following guidance strategy, which relies on the consideration of a pre-fixed allowable settling time and a pre-fixed allowable peak overshoot, related to allowable maximum cross-track error, in path following performance of the UAV. Simulation studies are presented to validate the better performance of the presented variable L1 guidance algorithm over the existing constant L1 algorithm in following reference paths containing segments with varied radii of curvature. © 2020 IEEE.