The field of biosensors has found great use for surface plasmon resonance (SPR), which has attracted attention for its multiple applications. With the goal of early cancer detection at the level of a single living cell, this research numerically investigates a very sensitive D-shaped fiber-optic biosensor based on surface plasmon resonance (SPR). The titanium oxide (TiO2) is coated on gold (Au), which is utilized as a thin-film plasmonic material in the suggested biosensor structure. The guiding of light in the fiber is modeled usingthe finite element technique (FEM) when six different types of healthy human cells and their malignant counterparts are exposed to its sensitive region. Refractive index (RI) differences between cancer cells and healthy cells are found through the analysis of the optical spectra and their amplitudes. This enables us to identify small changes in the optical characteristics of cells that could be a sign of pathogenic alterations. In this work, we concentrated on three forms of cancer: skin cancer (basal cell) and breast cancer (MDA-MB-231 and MCF-7). The results show which parameters are optimal to ensure that the sensor performs well when used to detect the three types of cancer under study. When the suggested sensor's performance is compared to SPR sensors that have previously been published in the literature, it becomes clear that our sensor offers great promise for early cancer detection.