A drive system of spherical robot was designed by which the horizontal obliquity of roll axe could be adjusted vertically to control turning and used to identify the roll axe as unique variable. Since only two control variables, the horizontal obliquity of roll axe and the rotate speed of drive motor, were used in the control model, the control strategy could be given without any complex operation. In order to deal with the problem of path tracking, the concept of relative curvature radius was introduced as a turning control index. Based on the existence and uniqueness theorem about plane curve theory in differential geometry, path tracking was actualized by adjusting horizontal obliquity of roll axe so as to make the track and path had the same relative curvature radius in the corresponding points with same arc length from respective original point. The arc length of the track from original point to the present position, needed to choose relative curvature radius in control process, could be obtained from the moving time, and no sensor was needed for measuring. The control strategy was proved to be correct for several especial values of relative curvature radius, and the feasibility of the control strategy was also validated by a simulation result.