Despite a large volume of preceding studies on the effects of free-stream turbulence (FST) on the aerodynamic forces of a square cylinder, limited knowledge is available regarding the evolutionary characteristics of flow with the change of turbulence integral length scale and turbulence intensity. This paper presents a systematic experimental study of the near wake flow and aerodynamic forces of a two-dimensional (2D) square cylinder in grid-generated turbulent flows and smooth flow. Particular attention is devoted to exploring the respective influences of turbulence integral length scale and turbulence intensity. The effect of FST with a higher-level turbulence intensity than previous investigations is also investigated. The near wake flow and aerodynamic forces are studied by particle image velocimetry (PIV) and synchronous pressure measurements. The proper orthogonal decomposition (POD) analysis is also performed to further understand the effects of FST on the coherent structures of fluctuating pressures around the square cylinder. The results show that the FST with a larger turbulence integral length scale and higher turbulence intensity can cause an increase in the vortex formation length, weaker vortex shedding process and interactions between the oppositely signed vortex rows. These changes lead to significant reductions in Reynolds normal and shear stresses, turbulence kinetic energy and fluctuating lift forces. A completely different flow pattern featured with flow reattachment and reseparation is interestingly captured on the square cylinder in a highly turbulent flow with a turbulence intensity of 20%. This flow pattern results in an obvious mean pressure recovery on the side surfaces and much larger pressure fluctuations near the leading edges and fluctuating torsional moments compared to those in smooth flow and turbulent flows with lower turbulence intensities.