Glass fiber‐reinforced polymers (GFRP) possess excellent structural qualities making it superior to steels and various allied materials in terms of strength and durability. The machining of GFRPs is relatively tough and slow on conventional machining systems. Also, tool life can be significantly reduced while working on such advanced materials with conventional machining processes. Lasers have been proved as a very efficient machine tool for cutting of several newly developed engineering materials. Low‐power lasers can be effectively used for ablating a thin layer or inducing customized surface structures on the target surfaces. Polymer‐reinforced composites act as a multilayered material having significant difference in melting and vaporization temperature between glass fibers and polymer matrix. In this experimental work, GFRP was used as a substrate material and a low‐power CO2 laser was utilized for engraving over a GFRP surface at different amounts of energy deposition. Unidirectional GFRPs were engraved by laser‐engraving process at three different defocusing positions with the overall objective to investigate the surface quality and engraving depth. To study anisotropic effects of the material, laser engraving was performed into two different directions, that is, along the fiber and perpendicular to fiber. Surface roughness and machined depth were investigated as a function of fiber direction. It was observed that surface roughness as well as ablation depth of the laser‐engraved surface hugely depend on fiber direction. It was also found that defocusing results in adverse surface conditions unlike other materials. Based on the results obtained, simple regression‐based mathematical models have been developed to predict engraved depth as a function of energy deposition. The developed models were validated for engraving depth up to 300 μm.