A new contact detection algorithm is proposed for the system of greatly differing particle sizes. The time complexity is linear with the particle number and the memory consumption is low. The algorithm has significant advantages to tackle the problems which have a large number of particles with arbitrary sizes and high density. Improved based on the NBS（no binary search）algorithm

the algorithm is more applicable to the polydisperse system with a multistep strategy than the NBS algorithm. With the particles divided into several groups and the detection progress divided into different steps

the particles in the same group can be considered as uniform and the size of grid can be set separately for different steps. As a result

the accuracy of the neighbour searching is increased. The number of the geometry resolution is decreased by setting the primary checking of the bounding boxes when the number of potential contact particles is more than 4. The number of groups is determined by a parameter previously chosen and is easily adjusted with different size gradations

so the algorithm has applicability to a wide range of particle systems. The properties of the algorithm are tested in several examples with different size gradation and the results show clear advantages over NBS algorithm.