Based on a new isospectral problem with three potential functions (q,r,s),a new Lax integrable hierarchy of evolution equations with an arbitrary function is obtained in this paper.When the potential,s,is put into differential functions,the hierarchy of equations can reduce to several kinds of systems of equations.By using the trace identity,their bi-Hamiltonian structures are given,and it is shown that they are integrable in the Liouville's sense.Moreover,the conserved densities and symmetries are also found.