  In this paper, we design and analysis a modified weak Galerkin (MWG) finite
element method for $\boldsymbol{H}(\mathrm{curl})-$elliptic problem. We first
introduce a new discrete weak curl operator and the MWG finite element space.
The modified weak Galerkin method does not require the penalty parameter by
comparing with traditional DG methods. We prove optimal error estimates in
energy norm. At last, we provide the numerical results to confirm these
theoretical results.
