Abstract: The problem of interpolation by a special kind of polynomial curves-Pythagorean hodograph curves （PH curves） in computer graphics is studied in this paper. Pythagorean hodograph curves enjoy a number of remarkable properties, such as, its offset curves have exact rational representations; the arc length function of a Pythagorean hodograph curve is simply a polynomial function of the curve parameter; and the lower degree Pythagorean hodograph curves have intuitive geometrical interpretation. By using complex analysis in representing parametric curves to avoid the complicated representation and fuzzy calculation, the cubic couple of Pythagorean hodograph is constructed, which satisfies C 1 Hermite interpolation conditions. This bicubic Pythagorean hodograph curves can deal with the inflexion flexibly and two cubic Pythagorean hodograph curves reaches C 1 continuous at the connection point. This propety overcomes the weakness of common cubic PH curves for being unable to dealing with connection points, because common cubic PH curves are constantly convex. The corresponding Bézier representations and the calculation of their control points can be easily obtained. In general, there are always four distinct interpolants and at least one has acceptable geometric shape characteristics. The obtained curve can be directly applied in the area of industry product design and milling machines.