The melting and freezing behavior of small-sized aluminum nanoclusters with radii ranging from 0.3 nm to 1.3 nm are investigated by molecular dynamics simulation. Based on the potential-temperature curves and heat capacity-temperature curves, the size dependences of melting point and freezing point are obtained and the results are analysed by the surface energy theory and small size effect. The results show a non-monotonic size-dependence of the melting temperature when the atom number of nanoclusters is less than 80. For those clusters with atom number more than 80, the melting and freezing point drop down monotonically with size decreasing. For some special cases, such as aluminum nanoclusters with atom number 27, the melting point is nearly 40 K higher than the bulk melting point. Besides, we observe a rather strong hysterisis of the liquid-solid transition, which states that it is much easier for a cluster to go from ordered to disordered than for the opposite process.