The construction of reliable global maps of vertical total electron content of the Ionosphere (Vertical TEC or VTEC Maps) is a useful but challenging task. A new technological route to construct global VTEC maps has been raised by us that COSMIC RO data points are collected during the past 24 hours in the sun-fixed coordinate system (local time and geomagnetic latitude) and then vertical TEC values within height range from 110km to 750km are calculated by numerical integration of electron density profiles at these RO points after quality control. At last, ordinary Kriging method is adopted to construct Global COSMIC TEC Maps with a grid resolution of MAGLat 2.5°× 2 h. Comparisons during the interval from DOY (Day of Year) 001, 2008 to 181, 2010 between Global COSMIC TEC Maps and IGS GIMs, from DOY 194, 2008, to 181, 2010 between Global COSMIC TEC Maps and OSTM/JASON-2 observations have been made, and differences are calculated for different seasons, local time and geomagnetic latitudes. It proves that COSMIC TEC Maps have good agreements with IGS GIMs and OSTM/JASON-2 observations, so COSMIC TEC Maps are accurate enough to be used to correct the ionospheric delay in GNSS systems. With further improvement on RO theories and commencement of new RO constellations in future, the quality and quantity of ionospheric RO data will be raised greatly with no doubt. Hence, it will be a much promising technology to apply ionospheric RO data to correct the ionospheric delay for GNSS systems.