In this article, we discuss the asymptotic stability and mean square stability of stochastic differential equations of fractional-order 1<α≤2. We have considered the family of stochastic differential equations with variable delay in the state. For proving our main results, we apply the Banach fixed point theorem and imposed the Lipschitz condition on nonlinearity. Finally, we present an example to illustrate the obtained theory. © 2021 Elsevier Ltd