Dynamic instability analysis of doubly-tapered cantilever composite beams rotating with periodic rotational velocity is conducted in the present work for out-of-plane bending (flap), inplane bending (lag) and axial vibrations. Rayleigh-Ritz method and classical lamination theory are used along with an energy formulation. Bolotin's method is applied to obtain the instability regions. To verify the dynamic instability analysis results, time responses are investigated at different locations of the instability region by using the Runge-Kutta method. A comprehensive parametric study is conducted in order to understand the effects of taper configurations and various system parameters including mean rotational velocity, hub radius, double-tapering angles and stacking sequences, on the dynamic instability characteristics of the composite beam. The composite material considered in the present work in numerical results is NCT-301 graphiteepoxy prepreg.