Novel flexible self-standing Cu-Al2O3 fibrous membranes have been successfully synthesized via electrospinning technique, and they exhibited high Fenton catalytic activities under neutral pH values. The copper species are distributed uniformly in the fibers in the form of Cu+ and Cu2+, which was responsible for the Fenton catalytic performance. Over 87% of BPA was degraded within 180 min in the membrane reactor using the 1 wt% Cu-Al2O3 membrane at neutral pH values with H2O2 addition. The membranes can continuously degrade BPA by batch in the membrane reactor without any additional separation process. The excellent catalytic performance, good flexibility of the membranes, and the facile preparation process make the membranes good candidates for novel heterogeneous Fenton catalysts.