This article proposes an approach to minimize the surplus parts in selective assembly with genetic algorithm. A grouping method is proposed considering the different tolerance ranges of parts, and the effect of part group assignment on assembly success rate is investigated. Based on the grouping method, a genetic algorithm with a specially designed two-dimensional chromosome structure is proposed to minimize surplus parts, and the fitness function of the solution and the constraints to be satisfied in the evolution process are investigated. The proposed selective assembly approach with the corresponding grouping method is further improved for the product assembly with multiple dimension chains. Through case studies, it is verified that the proposed approach is more competitive to improve the product assembly success rate and reduce the surplus parts.