The general five-axis toolpath, which consists of lines (or G01 commands) and arcs (or G02/G03 commands), is discontinuous in tangency or curvature at the transition points. The discontinuities will result in deteriorated machining efficiency and quality for the hybrid robot in high-speed machining. Therefore, toolpath smoothing techniques should be implemented. This paper proposes a semi-analytical C2 continuous corner smoothing method. Three types of tool position transitions are addressed considering the error tolerances, and tool orientation smoothing is addressed as a special case of spatial arc-arc smoothing on the unit sphere surface. Based on the analytical smoothing error expressions, the inserted B-splines are generated by numerical algorithms. In addition, the remaining path segments are converted into specially designed quintic B-splines for parameter synchronization, and a unified expression is derived to evaluate their margins. Finally, a feedrate scheduling and interpolation algorithm is proposed for trajectory generation. Simulations and experiments are performed on the TriMule-800 hybrid robot to verify the effectiveness of the proposed method for generating smooth motion in the operational space or joint space.