Entire tooth surface precise modeling and systematic analysis method for face-gear drives with an involute helical pinion are investigated. A modified imaginary shaper is mathematically modeled as the geometric design tool. The entire tooth surface of the face gear is determined analytically as the envelope to the family of imaginary shaper tooth surface. A practical method to determine the minimum and maximum radii of the face gear is developed. Addendum modification of the face gear is implemented mathematically based on the modified imaginary shaper to improve face-gear tooth-top thickness. Conical modification of the pinion is proposed to avoid contact between face-gear tooth-root fillet and the pinion tooth. Transverse pressure angle modification of the pinion is also proposed to avoid edge contact arising at inner-end and outer-end edges of face-gear tooth. Finite element models with nine pairs of teeth are employed for 3D contact finite element analysis to investigate the basic characteristics of face-gear drives, including meshing and tooth contact analysis, contact and bending stress analysis, contact ratio, transmission error, mesh stiffness, and sensitivity test. The helical face-gear drive is sensitive to rotation direction and shaft angle error. The presented geometric design method is illustrated and validated by numerical examples and trial manufacture.