We study cluster formation in a finite one-dimensional model system where the particles experience long-range attractive forces. The particles are first placed in equidistant positions by a repulsive potential, which then is turned off, and only a weak long-range potential acts between the particles. It is shown that the mean-square deviation in distance between the colloids at first increases due to normal Brownian motion, followed by a crossover to anomalous diffusion governed by the long-range forces. Moreover, we also found that the subsequent cluster formation could be described by a Poisson distribution. The results presented here may help us understand diffusion and cluster formation in one-dimensional systems.