The giant magnetoimpedance(GMI) effect of Co-rich microwires makes an opportunity to design sensitive GMI weak magnetic meter sensor. Optimization of magnetic meters needs to improve the GMI response, especially the field sensitivity of microwires. In this study, Co-rich amorphous microwires each with an average diameter of 32 μm are prepared by melt-extracted technique and their GMI characteristics are investigated at frequencies ranging from 0.1 to 10 MHz with and without bias direct voltage applied. Experimental results indicate that the GMI effect of these wires has asymmetric features with the increases of frequency and driving current. It is found that the intrinsic asymmetric GMI (AGMI) response results from the helical anisotropy and magnetization hysteresis of the Co-rich microwires. Furthermore, it is found that there is a pronounced improvement in AGMI response when a bias voltage is applied. In theory, the factor which induces an increase in circular magnetic field causes successive changes in magnetization reversal of the quickly quenched Co-rich microwires with multiple domains and helical anisotropy. As a consequence, the circular magnetization process is enhanced, leading to higher circular permeability and stronger GMI response. Meanwhile, a bias voltage inducing the given circular magnetic field reinforces the magnetization process in a certain direction, which intensifies the asymmetric characteristic of GMI response. For example, the asymmetric ratio between two impedance peaks rises from 1.46% to 12.06% at 1MHz and 3 mA after applying a 1 V bias voltage. Simultaneously, the circular field inclines the magnetization off the axial direction which makes the axially induced magnetization reversal more difficult and occur at a higher switching field. This effect broadens the linear impedance zone; however, it reduces the slope of the impedance with the external field and the field sensitivity increasing to some extent. The balance between these two sides proves that AGMI response is related to the magnetization reversal process which is sensitive to the circular magnetic field. Experimental results indicate that the field sensitivity rises from 616 to 5687 V/T with the impedance linear zone broadening from 0.65 to 1.16 when a 1 V bias voltage is applied, while it decreases to 4525 V/T when the bias voltage futher increases to 2 V at 10 MHz and 5 mA. This reveals that the GMI effect of these amorphous Co-rich microwires with high field sensitivity can be optimized by applying proper bias voltage.