Measurements of the total reaction cross section for 12-16C, 14-17N and 16-18 O on carbon target at intermediate energies were performed on RIBLL of HIRFL. A larger enhancement of σR for 15C was observed than that for its neighbors. The analysis of these data indicates possible existence of an anomalous nuclear structure in 15C.A new quantity was suggested as the criterion to distinguish anomalous structure nuclei from normal nuclei.