In this work, a study of hepatocellular carcinoma and normal livers in rats using nuclear magnetic resonance (NMR) based on superconducting quantum interference devices (SQUIDs) was presented. The time domain free induction decay signals, Sy(t), of cancerous liver tissue and control liver tissue of rats were measured to study the respective longitudinal relaxation rate T1-1 . The NMR data were fitted to [1-exp(-TBp/T1)] to derive the longitudinal relaxation times T1 for cancerous liver tissue and control liver tissue. It is found that T1, cancer of cancerous liver tissues is 2.3 times higher than T1, control of control liver tissues. Statistically the data suggest that T1, cancer/T1, control can be used to discriminate cancerous liver tissue from control tissue. Furthermore, differentiating cancerous tissues from control tissues was demonstrated using magnetic fluid phantoms as phantoms for cancerous and control tissues. The SQUID-detected NMR/MRI exhibits potential applications in clinical research.