A fast compact finite difference method, which discretizes the time Caputo derivative by using the H2N2 method, is proposed for fourth-order time fractional wave equations. In view of an increase of the computational efficiency, the exponential sum is used to approximate the kernel t1-γ, with the order reduction method and difference method adopted to discretize the spatial derivative term, thus proving the convergence of the scheme, with a spatial convergence order of four and a temporal convergence order of（3-γ）. Finally, numerical examples are used to verify the effectiveness of the theoretical analysis, and it is found that the CPU time required for this method is relatively short.