This paper is concerned with numerical approximations of stochastic wave equations driven by additive space-time white noise in one dimensional space. Convergence analysis and error estimates are presented for the numerical solutions based on the spectral Galerkin method with discretization in space variable. We obtain an estimate for the convergence rate. Comparing with the result of the finite difference approximation of Quer-Sardanyons and Sanz-Solé, the spectral Galerkin method enjoys

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... convergence rate. Our error estimate is comparable to the error estimate of another finite difference scheme recently constructed by Walsh. However, our analysis is much simpler and our algorithm is easier to implemented.