A novel microwave sensor for non-invasive blood glucose monitoring has been proposed in this paper. In order to inspect small variation in glucose density of capillary and evaluate the blood glucose level effectively for hypertension patient, the novel sensor should be sensitive with the dielectric constant of the detected medium, so one miniature monitoring antenna with a symmetrical network and electric properties may be promising choice contrast to the conventional microstrip patch, which doesn't demand for rigorous placement gesture. Referring to spiral structure and microstrip antenna, four-arm spiral microstrip antenna fed with a coaxial line is designed and simulated. It has a central frequency of 5GHz with a high quality factor and narrow bandwidth of 1.8%. To verify the supposed sensitivity and effectivity, some medium with different permittivity is attached on the surface and simulated. Small shift of the resonant frequency has been observed by virtue of the little changes of 1% in dielectric constant. The interesting phenomenon will be a good basis for further processing to extract the actual glucose level. More comparison and studies will be later investigated through fine simulations and experiments.