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We consider the time discretization of fractional stochastic wave equationwith Gaussian noise, which is negatively correlated. Major obstacles to designand analyze time discretization of stochastic wave equation come from theapproximation of stochastic convolution with respect to fractional Brownianmotion. Firstly, we discuss the smoothing properties of stochastic convolutionby using integration by parts and covariance function of fractional Brownianmotion. Then the regularity estimates of the mild solution of fractionalstochastic wave equation are obtained. Next, we design the time discretizationof stochastic convolution by integration by parts. Combining stochastictrigonometric method and approximation of stochastic convolution, the timediscretization of stochastic wave equation is achieved. We derive the errorestimates of the time discretization. Under certain assumptions, the strongconvergence rate of the numerical scheme proposed in this paper can reach$\frac{1}{2}+H$. Finally, the convergence rate and computational efficiency ofthe numerical scheme are illustrated by numerical experiments.

Strong approximation for fractional wave equation forced by fractional Brownian motion with Hurst parameter $H\in(0,\frac{1}{2})$