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The aim of this work is to propose an efficient numerical method for the solution of two‐dimensional multiterm time fractional diffusion‐wave equation. The Caputo time fractional derivatives of equation are approximated by a scheme of order scriptOfalse(τ3−αfalse), 1<α<2. To obtain a full‐discrete scheme, we apply the Legendre spectral element method on the spatial direction. Unconditional stability of the semidiscrete scheme and error estimate of full‐discrete method is presented. Numerical experiments are carried out to demonstrate the accuracy of the proposed method and to compare the results with the numerical solutions of other schemes in the literature. The results show that the present method is accurate and efficient. It is illustrated that the numerical results are in good agreement with theoretical ones.