SCII data set of positive-time finite-time Lyapunov exponent (FTLE) in the Gulf Stream calculated with velocity fields from Segment-Sol multi-missions d’ALTimétrie, Orbitographie et localisation précise/Data Unification and Altimeter Combination System (SSALTO/DUACS) absolute dynamic topography and absolute geostrophic velocity products. There are 7961 data sets: one per day from 7 January 1993 until 17 October 2014. Calculation of the FTLE is described in “Gulf Stream transport and mixing processes via coherent structure dynamics” by Yi Liu et al., submitted to JGR Oceans, 2017. The data can be uncompressed with standard tar commands. Data dimension in x and y are given in the first two lines of each set (1200x600), but are the same for each set. The grid coordinates are not included in the data set, but can be easily recreated knowing that the longitudes (x-direction) range from -89.875 (degree) to -30 (degree), and the latitudes (y-direction) range from 25.125 (degree) to 55 (degree). The data were written in a nested loop, with the y-dimension inside the x-dimension loop.