We devise a new simple loop algebra (G) over tilde (M) and an isospectral problem. By making use of Tu scheme, the multi-component Jaulent-Miodek (JM) hierarchy is obtained. Furthermore, an expanding loop algebra (F) over tilde (M) of the loop algebra (G) over tilde (M) is presented. Based on (F) over tilde (M) ,the multi-component integrable couplings system with two arbitrary functions of the multi-component Jaulent-Miodek (JM) hierarchy are worked out. The method can be applied to other nonlinear evolution equations hierarchies.