  In this paper, we propose a multi-component system of Camassa-Holm equation,
denoted by CH($N$,$H$) with 2N components and an arbitrary smooth function $H$.
This system is shown to admit Lax pair and infinitely many conservation laws.
We particularly study the case of N=2 and derive the bi-Hamiltonian structures
and peaked soliton (peakon) solutions for some examples.
