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.