Square sphere cannot be enveloped evenly by machining trajectory since the ball is processed in the traditional V-groove grinding method at a constant rotation angle. As a result, consistency of product batches is always affected. The work aims to propose a ball grinding processing method of variable turning curvature with single turntable, and motion state of the ball can be changed with curvature of groove. Based on pure rolling motion hypothesis, a relational model was developed for self-rotation angle and trajectory through kinematics analysis. G16 GCr15 steel ball was tested on the platform of a self-developed variable curvature grooved circular grinding machine. Process parameters such as slurry, load, rotation speed and grinding plate were changed. With roundness, roughness and batch consistency as indicators, the effects of single turntable variable curvature groove grinding were evaluated after rough grinding, fine grinding and polishing. Simulation results showed that uniform full envelope of trajectory on the ball could be achieved by optimizing arameters of the variable curvature trajectory. SD of trajectory symmetry reached 0.1986, average roundness was 0.095 μm, average surface roughness was 0.011 μm and consistency reached 0.17 μm, and final processing accuracy met requirements for G5 ball. Changes in groove raceway curvature enable self-rotation angle to change continuously between 0°~90°, further affects movement posture of ball and a fully-enveloped grinding trajectory is available. The grinding method can realize efficient and consistent ball processing, and accordingly, it has a high value of engineering application.