Laser rapid solidification experiments were performed on a Cu-Mn alloy to investigate its microstructure evolution as a function of growth rate. By taking transverse and longitudinal sections of the laser traces, the resulting morphology and the corresponding growth rate were quantitatively measured by scanning electron microscopy (SEM) and image analysis. As the growth rate increased, the morphological transition from dendrite --> fine cellular crystal --> banded structure --> fully cell-free microstructure, involving planar front growth, was clearly observed in the laser molten pool. By determining these transition conditions and comparing them with the predictions of theoretical models, we found that the origin of the banding can be well elucidated by the current Carrard-Gremaud-Zimmermann-Kurz (CGZK) phenomenological model, while the critical condition of planar front growth was in reasonable agreement with Mullins-Sekerka (M-S) stability theory.