A localized space-time method of fundamental solutions(LSTMFS)is extended for solving three-dimensional transient diffusion problems in this paper.The interval segmentation in temporal direction is developed for the accurate simulation of long-time-dependent diffusion problems.In the LSTMFS,the whole space-time domain with nodes arranged is divided into a series of overlapping subdomains with a simple geometry.In each subdomain,the conventional method of fundamental solutions is utilized and the coefficients associated with the considered domain can be explicitly determined.By calculating a combined sparse matrix system,the value at any node inside the space-time domain can be obtained.Numerical experi-ments demonstrate that high accuracy and efficiency can be simultaneously achieved via the LSTMFS,even for the problems defined on a long-time and quite complex computational domain.