Based on the nonlinearization of Lax paris, the Korteweg-de Vries (KdV) soliton hierarchy is decomposed into a family of finite-dimensional Hamiltonian systems, whose Liouville integrability is proved by means of the elliptic coordinates. By applying the Abel-Jacobi coordinates on a Riemann surface of hyperelliptic curve, the resulting Harnil-tonian flows as well as the KdV soliton hierarchy are ultimately reduced into linear superpositions, expressed by theAbel-Jacobi variables.