To track maneuvering target, cognitive radar could adjust its transmitted waveforms to obtain some sustainable or robust information of target. We propose a novel adaptive waveform design method based on matrix-weighted Interacting Multiple Model fusion (AMIMM) for tracking maneuvering target. The target state is modeled via the multi-model idea, and the tracking framework is formulated by using the matrix-weighted multi-model fusion in lieu of probability-weighted way. The fused covariance matrix of state estimation is selected as the ellipse metric, and its ellipse parameters could be obtained by using EigenValue Decomposition (EVD). Finally, according to the fused covariance matrix-related ellipse parameters, the fractional Fourier transform (FrFT) is utilized to rotate the measurement error ellipse to make them orthogonal to each other, and obtain the adaptive waveforms. Simulation results show that compared with several current algorithms, our algorithm could further improve the tracking accuracy and robustness.