This paper evaluates the effect of stress-relieving heat treatment on the AlSi10Mg alloy prepared by additive manufacturing using the Laser Powder Bed Fusion (L-PBF) with print parameters: 370 W, 1400 m/s, and 50 μm. The as-built state and four different annealing modes (240 °C/2 h, 240 °C/6 h, 300 °C/2 h, and 300 °C/2 h/water-quenched) are investigated. To determine the effect of the annealing mode on the mechanical properties of the L-PBF AlSi10Mg alloy, heat-treated samples were compared with the as-built state and with each other. The mechanical properties of the samples were determined by tensile and hardness tests. The strength in the as-built state is 488 MPa, depending on the method of heat treatment, the strength values range from 296 MPa to 417 MPa, and the HV10 hardness values are in accordance with the measured strength values. Furthermore, the microstructure of the samples was investigated by scanning electron microscopy (SEM) analysis, which was then linked to the measured mechanical properties. The composition of the microstructure of the alloy and its influence on the mechanical properties were determined by energy dispersive spectroscopy (EDS) analysis. Furthermore, the differences between the individual heat treatments in comparison with the as-built state were analyzed and the phenomenon of decomposition of the silicon network after reaching specific temperatures was discussed and confirmed. The paper evaluates the effect of dwelling time on stress relief annealing. It was found that if annealing at intermediate temperatures of 240 and 300 °C is applied, changes in structure and mechanical properties are more temperature- than dwell-time-dependent.