Abstract <p>In this work, we investigate a multicontinuum time-fractional diffusion-wave model, which is derived through the application of the multicontinuum homogenization method. Using the Caputo time-fractional derivative, we adopt a fully discrete finite-difference scheme for the temporal discretization. Moreover, to decrease the dimensionality of the discrete system, we develop a coarse-grid approximation constructed within an online generalized multiscale finite element framework. The online GMsFEM framework consists of two components: an offline phase and an online pha- se. During the offline phase, local spectral problems are solved, and the corresponding leading eigen- vectors are employed to build the multiscale basis functions. The algorithm’s accuracy is improved in the online phase by incorporating additional online basis functions, which are generated using the local residual information. By incorporating online basis functions, we enhance the offline multiscale space and efficiently diminish errors. We present the relative errors between the multiscale solution and the reference solution for varying numbers of offline and online multiscale basis functions. The numerical results indicate that the online multiscale method achieves higher accuracy than the offline method while using only a small number of degrees of freedom on the coarse grid.</p>