In this paper, an LMI-based design is proposed for observer control problem of nonlinear fractionalorder systems subject to time-variable delay, where the delay function is non-differentiable, but continuous and bounded. Our novel technique is based on a new lemma concerning Caputo derivative estimation of quadratic functions. In this proposed approach, delay-dependent sufficient conditions in terms of linear matrix inequalities are obtained for the design state feedback controller and observer gains. A simulation-based example is given to illustrate the effectiveness of the theoretical result