The layer Hall effect (LHE), originating from layer-locked Berry curvature, extends the scope of the Hall effect family and offers promising prospects for quantum layertronics. Here, a light-induced quantum anomalous layer Hall effect (QALHE) in antiferromagnetically coupled van der Waals (vdW) multilayers is proposed. Within a hexagonal lattice model, circularly polarized light is found to enable precise control over the layer-locked Berry curvature distribution, which causes asynchronous quantum anomalous Hall effects (QAHEs) in distinct layers, manifested as layer-locked quantized Chern numbers. The interlayer asynchrony gives rise to a stepwise evolution of the total Chern number with an increase in light intensity. First-principles calculations confirm the QALHE in experimentally feasible VSi2N4/VSiGeN4 heterobilayers, as well as in VSi2N4 tri- and tetralayers, with Chern numbers up to 2, 3, and 4. Our findings bridge Floquet engineering with layer-locked transport phenomena, offering realistic pathways for nonequilibrium topological state manipulation in two-dimensional quantum materials.