A planar metamaterial (MM) mimicking electromagnetically-induced transparency (EIT) effect is demonstrated numerically and experimentally in the microwave region. The structure of MM is a periodicity of ring and zigzag spiral resonators, in which each resonator can be excited directly by the external field. By matching the characteristic resonance frequencies of two resonators, the coupling of two bright modes appears, leading to an EIT effect with a transparency peak at 4.86 GHz. Although the geometry of the structure is not perfectly symmetric, the proposed electromagnetically-induced transparency metamaterial (EIT-MM) is insensitive to the polarization of incoming wave. Furthermore, the EIT-MM exhibits a strong dispersion behavior, which leads to a high group index of 2785 and a group delay of 0.83 ns. Our work might be useful to potential applications using EIT-MM such as modulators, filters and sensors.