Build time estimation for parts is very important for the design, process planning & optimization and price quotation in Additive Manufacturing (AM). However, the related factors are numerous and have complicated interrelations with each other. This makes it difficult for current methods to obtain an accurate estimation model without inputting a relatively large quantity of data on part specifications, machine setup, processing details or production requirements. To construct build time estimation models more rapidly and simply to meet the needs of price quotation, design, process planning and optimization in AM, with acceptable accuracy by inputting less data, this paper introduces an integrated adaptive modeling method derived from Grey Theory. A numerical example used for comparing it with current modeling methods and a case study of building an estimation model for an FDM machine have evidenced the availability and advantages of this proposed modeling method. The average estimation accuracy is within 10%, which is acceptable for many application contexts and better than several current parametric and analogical models.