In this article, a kind of nonlinear wave model with the Caputo fractional derivative is solved by an efficient algorithm, which is formulated by combining a time second-order shifted convolution quadrature (SCQ) formula in time and a mixed element method in space. The stability of numerical scheme is derived, and an optimal error result for unknown functions which include an original function and two auxiliary functions are proven. Further, the numerical tests are conducted to confirm the theoretical results.