<p>This paper proposes a generalized quasi-reversibility regularization method for solving an inverse spatial source problem in a time-fractional diffusion-wave equation by using an additional final time observation. Based on the series formulation of the spatial source, we obtain an error estimate between the regularized source solution and the exact source component. For the quasi-reversibility regularized problem, we propose a fully discrete numerical algorithm by using the backward Euler convolution quadrature scheme for discreting the time-fractional Caputo derivative and the piecewise linear finite element scheme for dealing with the second-order elliptic operator. With the help of a semi-discrete regularized problem, the convergence estimate for the numerical source solution in a fully discrete regularized problem approaching to the exact source function is provided in terms of a certain reasonable assumptions to the given data and a suitable choice of the regularization parameter according to the noise level and stepsizes. The numerical results for six examples are given for one- and two-dimensional cases to show the efficiency of the proposed regularization method.</p>