Summary: In this article, we consider initial and boundary value problems for the diffusion-wave equation involving a Caputo fractional derivative (of order \(\alpha\), with \(1 < \alpha < 2\)) in time. A novel finite difference discrete scheme is developed for using discrete fractional derivative at time \(t_n\) in which some new coefficients \((k + \frac{1}{2})^{2 - \alpha} -(k - \frac{1}{2})^{2 - \alpha}\) instead of \((k + 1)^{2 - \alpha} - k^{2 - \alpha}\) are derived. Stability and convergence of the method are rigorously established. We prove that the novel discretization is unconditionally stable, and the optimal convergence orders \(O(\tau^{3 - \alpha} + h^2)\) both in \(L_2\) and \(L_\infty\) are derived, where \(\tau\) is the time step and \(h\) is space mesh size. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.