In this article, we consider finite difference schemes for two dimensional time fractional diffusion-wave equations on an annular domain. The problem is formulated in polar coordinates and, therefore, has variable coefficients. A compact alternating direction implicit scheme with O (τ 3 - α + h 1 4 + h 2 4) accuracy order is derived, where τ, h1, h2 are the temporal and spatial step sizes, respectively. The stability and convergence of the proposed scheme are studied using its matrix form by the energy method. Numerical experiments are presented to support the theoretical results.