This study systematically investigates the effects of laser power (1.50–2.00 kW) and travelling speed (8–11 m/min) on microstructure and mechanical properties of lap joints fabricated by continuous-wave laser welding of newly developed Al – 7Mg alloy. Optical microscopy (OM) and electron backscattered diffraction (EBSD) analysis revealed a non-equilibrium eutectic structure in the weld zone (WZ), comprising equiaxed and columnar grains. The heat-affected zone (HAZ) exhibited grain coarsening and partial melting in the boundaries, due to the melting of Al3Mg2 compound. Porosity-free joints were achieved under optimal parameters (laser power of 1.75 kW at a travelling speed of 9 m/min as well as laser powers of 1.50 kW and 2.00 kW at a travelling speed of 10 m/min). These joints had good tensile-shear properties. Also, laser power of 1.75 kW and travelling speed of 9 m/min could be known as satisfyingly optimized conditions, causing superior tensile-shear performance of the laser joint (tensile-shear strength of ∼225 MPa and elongation of ∼30 %). This issue underlined the importance of process optimization. Micro-hardness measurements showed the greater hardness of WZ than HAZ and base metal (BM), caused by eutectic structure of WZ. The hardness of HAZ was lower than that of BM, attributed to the HAZ softening. Fractography revealed a ductile-to-brittle transition with increasing laser power, driven by grain coarsening. In addition, the failure took place at the WZ/HAZ interface during tensile-shear test. Remarkably, no solidification or hot cracks were observed in the laser welds. The absence of solidification cracks and therefore outstanding laser weldability of Al – 7Mg alloy are primarily referred to lower solidification and cooling rates associated with continuous-wave laser welding, favorable eutectic healing mechanism, and preservation of magnesium content within the weld pool due to presence of calcium in the chemical composition of Al – 7Mg alloy. This article suggests that it is momentous to effectually optimize or modify laser welding process to reach laser welds with excellent performance in Al – 7Mg alloys employed in lightweight structural applications.