The laser ablation process is an indispensable tool in precision micromachining for fabricating micro/nanostructures with specific geometries and regulating physicochemical properties on target surfaces. However, the absence of studies on the effect of laser parameters on texturing formation and surface microstructure makes process control and the optimization of surface texturing challenging. In this study, a nanosecond pulsed laser process was employed to create the micro-texturing on the Al alloy surface, emphasizing the effect of process parameters on surficial grain structures and texturing formation. A three-dimensional (3D) heat transfer model based on the finite element (FE) method was developed to numerically visualize the shape-dimensional evolution of micro-texturing during laser ablation. A simplified but effective moving laser heat source model was proposed to predict the dynamic spatial and temporal distributions of heat generation and transfer. Material removal, which was dominated by surface evaporation in the pulsed laser process, was achieved using the element deletion method. Under various laser parameters, the model-predicted cross-sectional groove profiles agreed well with experimental measurements. In addition, the effects of laser power and scanning speed on the groove morphologies were investigated. The experimental findings and numerical models established in this study will provide guidance for precisely controlling pulsed laser parameters to achieve desired texturing structures and dimensions.