This article provides a graphical parameter tuning method of PIλ controllers for fractional-order time-delay systems.First,the complete stabilizing region of PIλ controller in proportional-integral plane,for a fixed λ,is determined in terms of a graphical stability criterion applicable to fractional-delay systems.Then,the stabilizing region is maximized analytically with respect to parameter λ to expect the most various behaviors of the closed-loop systems.Finally,by defining appropriate functions relative to the requirements of gain and phase margins,the curves in the maximized stabilizing region satisfying the pre-specified gain and phase margins are drawn,which releases a flexible parameter tuning procedure.Numerical examples are given to illustrate the design steps.