In this paper, we study the Kropina transformation of exponential (α,β)-metric F=α\exp(s), s:=β/α. We characterize the conditions under which this class of (α,β)-metric is locally projectively flat, locally dually flat, and Douglas metric. Based on, we show that the Kropina transformation of an exponential (α,β)-metric is locally projectively flat, locally dually flat and Douglas metric if and only if the exponential (α,β)-metric is locally projectively flat, locally dually flat and Douglas metric, respectively.