This paper presents a convolution quadrature time-domain boundary element method for fluid-elastic half space. Application of convolution quadrature method (CQM) to time-domain boundary element method (BEM), which is called CQ-BEM, can help improve numerical stability of time-stepping procedure. However, the conventional CQ-BEM for fluid-elastic half space has two disadvantages. First, it requires much memory to evaluate retarded potentials of time-stepping procedures. Second, it is difficult to couple both boundary integral equations for fluid and elastic half space with time-domain boundary conditions on fluid-elastic interface directly. The formulation presented herewith improves these disadvantages by transforming boundary values in time-domain into Fourier-domain. As numerical examples, air-coupled ultrasonic simulation is shown to validate the presented method.