Surface plasmon resonance-based optical fibre sensors are regarded as a highly developed and highly advanced sensing optical technology. These sensors have many different applications in different fields, such as medical diagnostics, the detection of chemical and biological analysts, electrochemical sensing of state of charge of super capacitor, environmental monitoring, etc. In this regard it is very important to study the optical behaviour and various parameters influencing its behaviour to construct a sensor with a desired performance. For this reason, it is required to fine-tune various parameters by analyzing its behaviours on a fast-track basis. Therefore, a powerful simulation tool is required to analyze various influencing factors some of which can be mentioned that are field intensities (magnetic and electric), effective refractive index, etc. In this paper we would like to demonstrate the modelling and numerical simulation carried out on an extremely sensitive surface plasmon resonance-based D-shaped optical fibre sensor furnished with silver gratings coated with titanium dioxide (TiO2) layer on the top. Here, titanium dioxide coating acted as a sensing sheet, whereas the free electrons present in metal generated surface plasmons excitation with the help of momentary waves on the surface of the fibre. The variations in refractive index (RI) were then determined by monitoring the resonance absorption peaks. With the application of the finite element method, the SPR fibre sensor was optimized allowing to investigate D-shaped fibre’s structural parameters as well as silver gratings. Using the same method, it was analyzed what might be the consequences due to variation on the thickness of titanium dioxide layer on the overall sensor sensitivity (S). The final simulation result indicated that the sensor sensitivity was significantly enhanced by adjusting appropriate thickness of the titanium dioxide-coated silver gratings.