Using complex analysis and curve integration, the construction of PH quintic which satisfies Hermite interpolation conditions is studied in this paper and its corresponding Bézier representation is derived. The PH quintic has continuous unit tangents and signed curvature, and its arclength function is the polynomial of its parameter. The PH quintic has offset curve that admits exact rational algebraic representation, intuitive geometrical interpretation and can flexibly deal with inflection point.