In this paper, we have studied the quadrature error reduction for the single drive 3-axis MEMS Gyroscope. There was a limitation of the previous study which is the z-axis quadrature error was large. To reduce this value, design methodologies were presented. And the methodologies included a different mesh application, z-rate spring structure change, and mass compensation for balancing of the structure. We conducted the modal analysis, drive mode analysis and sense mode analysis using COMSOL Multiphysics. As a result, a drive resonant frequency was 26003 Hz, with the x-sense, y-sense, z-sense being 26749 Hz, 26858 Hz, 26920 Hz, respectively. And the Mechanical sensitivity was computed at 2000 degrees per second(dps) input angular rate while the sensitivity for roll, pitch, and yaw was computed 0.011, 0.012, and 0.011 nm/dps respectively. And z-axis quadrature error was successfully improved, 2.78 nm to 0.95 nm, which the improvement rate was about 66 %.