White-light scanning interferometry (WLSI) is often used to study the surface profiles and properties of thin films because the strength of the technique lies in its ability to provide fast and high resolution measurements. An innovative attempt is made in this paper to apply WLSI as a time-domain spectroscopic system for localized surface plasmon resonance (LSPR) sensing. A WLSI-based spectrometer is constructed with a breadboard of WLSI in combination with a spectral centroid algorithm for noise reduction and performance improvement. Experimentally, the WLSI-based spectrometer exhibits a limit of detection (LOD) of 1.2 × 10-3 refractive index units (RIU), which is better than that obtained with a conventional UV-Vis spectrometer, by resolving the LSPR peak shift. Finally, the bio-applicability of the proposed spectrometer was investigated using the rs242557 tau gene, an Alzheimer's and Parkinson's disease biomarker. The LOD was calculated as 15 pM. These results demonstrate that the proposed WLSI-based spectrometer could become a sensitive time-domain spectroscopic biosensing platform.