In a communication system, the group delay variation (GDV) causes the distortion of signal and the degradation of symbol error rate. Usually, the compensation of group delay (GD) utilizing positive group delay (PGD) results in further propagation delay. Therefore, this research studies the negative group delay (NGD) behavior of metamaterial. Through analyzing the effects on GD caused by poles and zeros of circuit, the group delay circuit capable of switching between NGD and PGD is presented. Further, adjustable negative group delay circuits (NGDCs) are designed based on the concept of poles and zero. The NGD generated by NGDC is used to achieve the equalization of GD and recover the distorted signal in time domain. Additionally, owing to the limited frequency band of communication, a filter with high selectivity is required to utilize the available bandwidth. The character of left-handed metamaterial is applied to the design of filter for reducing the size and cost of traditional microstrip line filters with high selectivity. Under the balanced condition, composite right/left-handed (CRLH) transmission line behaves right- and left- handed characteristics in different frequency bands. Thus, a coplanar waveguide (CPW) filter with high selectivity, size reduction and low cost is presented utilizing such a CRLH structure.