Abstract: Aiming at the situation of uneven graph frequency distribution, a design method of non-uniform graph filter banks is proposed. Firstly, according to the property of graph frequency distribution, the non-uniform analysis filter of well frequency selection characteristics and well sparse property in vertex domain is need to be designed. The method of it is that design the non-polynomial form filter with low order by approximating the polynomial form with high order. Secondly, given the non-uniform analysis filter and sub-band signal, the reconstruction problem could be formulated a least square problem. To avoid the high calculation cost of matrix inverse in this optimization when graph is with large scale, a precondition gradient descent method is proposed to solve this problem and which can be implemented in distributed manner. Numerical results show that the non-uniform graph filter banks proposed in this paper can achieve perfect reconstruction and have well frequency selection characteristic and localized property in vertex domain. Compared with existing iteration methods, the proposed algorithm has the faster convergence rate and lower calculation cost.