Pythagorean-hodograph (PH) curve is widely used in curve modeling because of its advantages in arc length and equidistant curve calculation.This paper discusses the G2 continuous blending of cubic PH curves under total arc length constraint.Given three points including two end control points and a joint point,construct two cubic PH curves such that they interpolate the end control points and are G2 continuous at joint point with prescribed total arc length.It can also be regarded as a curve extension problem.According to the arc length formula of cubic PH curve and the condition of G2 blending,the problem is transformed into a constrained minimization problem.Several examples are served to illustrate our method.