Abstract: In engineering practice, glass fiber reinforced polymer (GFRP)-concrete composite beams usually fail as a result of larger damages, and hence it is of great significance to study the damage process. In order to study the damage characteristics of such components, four-point bending loading tests were carried out for a GFRP I-beam and six GFRP-concrete composite beams connected by different bolts, and the whole process was monitored by an acoustic emission (AE) device. On the basis of the phase-space reconstruction of the AE energy signals, the fractal dimension of AE energy signals were calculated in each loading stage. The results show that the time serials of AE energy is of fractal characteristics. The dimension can well describe the complete damage stages; The evolution of the fractal dimension curve of AE energy time series is summarized: the mode in pure bending section is “early peak” to “low amplitude fluctuation”; the mode in shear span area is “low amplitude fluctuation” to “continuous high amplitude fluctuation”; by comparing the phenomenon of loading process of test beam with the evolution of fractal dimension value, the “sustained high amplitude fluctuation” of the fractal dimension can be regarded as the precursor of the instability of the test beam. According to the dimension, the possibility of “early warning” was proposed. Early warning points can be identified when there is enduring high-amplitude fluctuation for corresponding fractal dimension. The bearing capacity of the structure has reached about 70% of the allowable extreme, suggesting necessary intensified monitor.