Due to its wide application in problems such as transportation, stochastic games and economic equilibrium, the numerical algorithm for stochastic variational inequality has attracted extensive attention. By means of the stochastic approximation method, a forward-backward algorithm with line search for solving stochastic variational inequalities is proposed. At each iteration, the algorithm only needs to calculate one projection onto the closed convex set, and does not require the information about the Lipschitz constant, thus avoiding a lot of unnecessary computation. Under mild assumptions, it is proved that the sequence generated by the algorithm converges almost surely to the solution of the stochastic variational inequality problem. With the help of natural residual function, the results of sublinear convergence rate and the iteration complexity of the algorithm are also obtained. Finally, the feasibility and effectiveness of the algorithm are verified by some numerical examples.