This paper presents a modified design of a high-resolution fiber optic sensor that operates on the surface plasmon resonance effect. The sensor is based on the well-known method of generating surface plasmons with the help of an inscribed tilted fiber Bragg grating that excites the cladding modes. Because the original design solution used a polarizing fiber, it was possible to significantly improve the stability of the sensor readings. The specialized mathematical apparatus was used to determine the surface plasmon resonance spectral position. It was experimentally shown that the limit of detection to the refractive index of such a sensor is 2 × 10−6 refractive index units. The sensor's response to the investigated medium temperature change is presented and analyzed. The high resolution of the sensor in detecting protein molecules was demonstrated. Such sensors open wide perspectives for their application in real high-sensitivity sensor systems as biosensors for immune analysis in medical diagnostics.