The conventional methods for the diagnosis and treatment of cancer, based on surgical, chemical, and radiation processes, are expensive, time-consuming, and painful. Therefore, research in this field has been devoted to developing precise, cost-effective, and rapid techniques for early cancer detection. In recent decades, optical biosensors have become powerful tools for identifying various biological and non-biological analytes. Optical biosensors possess features such as high sensitivity and accuracy, non-invasiveness, label-free detection, and compact size. The surface plasmon resonance (SPR) phenomenon is one of the optical phenomena created by the absorption of photons at the metal/dielectric interface. The key characteristic of SPR is its sensitivity to environmental changes, meaning that placing normal and cancerous tissue samples on the sensor will result in different sensor responses. Recently, studies in this field have progressed towards using the SPR phenomenon in metamaterials. In this design, a metamaterial structure with SPR properties is utilized to create a plasmonic biosensor capable of detecting samples of normal and human cancerous liver tissues. The main idea is to detect normal liver tissue from cancerous liver tissue with high sensitivity. The designed sensor is based on the metamaterial structure and surface plasmon resonance enhancement. The samples used in this sensor include several liver tissue samples from various patients, including normal and disease-free samples, metastatic liver samples, non-metastatic liver samples, carcinoma liver samples, and non-carcinoma liver samples. In fact, in the proposed sensor in this design, metastatic tissue can also be distinguished from carcinoma tissue.