The stochastic comparisons of parallel and series system are worthy of study. In this paper, we present some stochastic comparisons of parallel and series systems having independent components from Gumble distribution with two parameters (one location and one shape). Here, we first put a condition for the likelihood ratio ordering of the parallel systems and second we use the concept of vector majorization technique to compare the systems by the reversed hazard rate ordering, the hazard rate ordering, the dispersive ordering, and the less uncertainty ordering with respect to the location parameter.