In this research, single-mode fiber laser welding process of 2 mm 6013 aluminum alloy are carried out based on response surface method. The relationship between the process parameters such as laser power, welding speed, and defocused position of the laser beam with the output responses such as top melt width, back melt width, back-to-top width ratio and fusion zone area are established in terms of 3 D response surface models. The models are significant and fit well. The influence of process parameter on the geometric characteristics of welded joints and the microstructure properties of typical welds are analyzed. The results show that the laser power is positively correlated with back melt width, back-to-top width ratio and fusion zone area; welding speed is negatively correlated with all output variables; the defocused position is positively correlated with top melt width and fusion zone area, while negatively correlated with back-to-top width ratio. There is an obvious interaction between laser power and defocused position in the regression model of back-to-top width ratio. The single-mode fiber laser can realize the full penetration of 2 mm 6013 aluminum alloy under the process matching of low power and high welding speed, and the section melting width of the welded joint is narrower and the micro grain size is small. Its tensile strength and section elongation are 315.5 MPa and 12.3%respectively, which can reach 90% and 42% of the base metal.