Abstract: In a diffusion-limited aggregation model with spin freedom in each particle,morphology and fractal dimension D_f of magnetic clusters grown on two-dimensional triangular lattices are investigated with Monte Carlo study.Power-law interaction J/r^a is used.It shows that as α≥5 patterns of clusters hardly vary with J.Their fractal dimensions range from 1.50 to 1.70.With decreasing α,morphology evolution of clusters exhibits rich behaviors.Fractal dimension D_f changes continuously from about 1.20 to 1.90.