We employ a linear Bayes procedure to estimate the unknown parameter of the uniform distribution R(-\theta,\theta) and propose a linear approximate Bayes estimator (LABE) for \theta, which has a closed analytic solution form and is convenient to use. Numerical simulations indicate that the proposed LABE is close to the ordinary Bayes estimator (BE), which is calculated by numerical integration and the so-called brute-force method as well. Furthermore, we compare the proposed LABE with the Lindley's approximation. The superiorities of the LABE over the classical estimators are also established in terms of the mean squared
error (MSE) criterion.