<p>A test of central symmetry of a functional random variable is proposed. We use the characterization of symmetry via the characteristic functional, that is, we use the fact that the characteristic functional of a symmetric random function is a real-valued functional. Hence, we construct a Cramér–von Mises-type test of the hypothesis that the imaginary part of the characteristic functional vanishes. The test statistic assumes a relatively simple form if we use a Gaussian measure to construct the test. As the test statistic is a degenerate <i>U</i>-statistic, we must use a wild bootstrap to obtain approximate critical values under the null hypothesis. An alternative approach based on a two-sample test for functional data is compared with our test procedure. Several simulations illustrate the performance of the proposed test.</p>