In this paper, a posteriori error estimate of a weak Galerkin (WG) finite element method for solving H(curl)-elliptic problems is designed and analyzed. Firstly, a WG method for H(curl)-elliptic problems and a corresponding residual type error estimator without stabilization term will be introduced. Secondly, the reliability of the error estimator is proved by presenting that the stabilization term is controlled by error estimator. Then, the efficiency of the error estimator is provided by using standard bubble functions. At last, some numerical results are carried out to show the performances of the error estimator in both uniform and adaptive meshes.