The microscopic lattice kinetic model of aging process was build, using the coupling of the theory of microscopic elastic energy and microscopic diffusion equation. Taking a binary cubic model alloy with 14% (solute atom percent) as a example, the coarsening behavior of coherent precipitants was simulated. The results show that the main precipitation mechanism is nucleation and growth, while transient spinodal decomposition can also occur; In the presence of coherent mismatch, plate-like precipitants are formed, and tend to align along the elastically soft directions. During its coarsening process, particles lying in the soft directions grow and coarsen further, particles lying out of the soft directions dwindle. The coarsening process of the particles sitting in the same row or column obey that smaller particles shrink and larger ones grow.