Humic acid (HA) has a high complexation ability with metal ions due to its functional groups. In this study, 11 synthetic humic-like acids (SHLAs) were prepared under varying abiotic humification conditions: precursor species (glycine-catechol and glycine-catechol-glucose), precursor concentrations (from 0.25 M:0.25 M to 1 M:1 M), pH (6–8), temperature (25–45 °C) and mass of MnO2 catalyst (1.3–2.5% w/v). The effect of the varying humification conditions on the complexation ability of the SHLA for Cu2+ were investigated together with the relationships between Cu complexation ability and the structure of the SHLAs (elemental composition, type and content of functional groups, AL/AR, E4/E6). Conditional stability constants (log K) of the SHLAs ranged from 6.00 to 6.42 and complexation capacities ranged from 1.76 mmol/g to 2.61 mmol/g. SHLAs synthesized at lower temperature (25 ℃), pH 8, low precursor concentrations (glycine:catechol= 0.25 M:0.25 M) and a larger proportion of catalyst (2.5% w/v) had a larger copper complexation ability. Log K values of SHLAs had significant positive correlations with carboxylic carbon (r = 0.671, p < 0.05), carboxylic group content (r = 0.890, p < 0.01) and O/C ratio (r = 0.618, p < 0.05), and significant negative correlations with aliphatic carbon (r = −0.616, p < 0.05), total C (r = −0.685, p < 0.05) and total H contents (r = −0.654, p < 0.05). Complexation capacities had a significant positive correlation with total N (r = 0.826, p < 0.01) and a significant negative correlation with C/N ratio (r = −0.823, p < 0.01).