In this study, we report a convenient label-free fluorescence biosensor for the detection of acid phosphatase based on the aggregation-caused quenching of graphene quantum dots (GQDs). The fluorescence of GQDs could be quenched by poly-(dimethyl diallyl ammonium chloride) (PDDA); the high efficiency of the quenching was caused by the non-covalent binding of positively charged PDDA to negatively charged GQDs through electrostatic interactions, aggregating to form a GQDs-PDDA complex. Addition of sodium hexametaphosphate (NaPO₃)₆ could effectively turn on the quenched fluorescence due to the stronger electrostatic interactions between positively charged PDDA and negatively charged (NaPO₃)₆. The introduction of acid phosphatase (ACP) would lead to the breakdown of (NaPO₃)₆ into small fragments and disassemble the complex of PDDA-(NaPO₃)₆. As a result, the recovered fluorescence could be quenched again by the addition of ACP. Quantitative evaluation of ACP activity in a broad range from 30 nU mL⁻¹ to 420 nU mL⁻¹ with a detection limit of 12 nU mL⁻¹ can be achieved in this way, endowing the assay with sufficiently high sensitivity for practical detection of ACP in human serum.