Uneven terrain walking is one of the important premises for biped robots to serve people. However, it is one of the key challenges for biped robots walking on a slope. In this paper, a universal method to generate patterns for biped robot walking on a three-dimensional (3D) slope is proposed. Different from most researches, which only focused on the specific walking directions on a slope as across or along a slope, the proposed method is applied to biped robots for all directions walking on a slope. First, unification of parameters for biped walking on a 3D slope is designed. Second, walking patterns based on dual linear inverted pendulum method (DLLIPM) on a 3D slope are generated. Finally, the effectiveness of the universal pattern generator is verified through simulations.