In this paper, nonconforming mixed finite element method is proposed to simulate the wave propagation in metamaterials. The error estimate of the semi-discrete scheme is given by convergence order $\mathcal{O}(h^2)$, which is less than 40 percent of the computational costs comparing with the same effect by using Nédélec-Raviart element. A Crank-Nicolson full discrete scheme is also presented with $\mathcal{O}(τ^2 + h^2)$ by traditional discrete formula without using penalty method. Numerical examples of 2D TE, TM cases and a famous re-focusing phenomenon are shown to verify our theories.