Taxicab plane geometry and Cinese-Checker plane geometry are non-Euclidean and more practical notion than Euclidean geometry in the real world. The ${alpha}$-distance is a generalization of the Taxicab distance and Chinese-Checker distance. It was first introduced by Songlin Tian in 2005, and generalized to n-dimensional space by Ozcan Gelisgen in 2006. In this paper, we studied the isoperimetric inequality in ${alpha}$-plane.