Superconducting nanowire-based single-photon detectors (SNSPDs) are promising devices, especially with unrivalled timing jitter ability. However, the intrinsic physical mechanism and the ultimate limit of the timing jitter are still unknown. Here, we investigated the timing jitter of the SNSPD response to different excitation wavelengths from visible to near-infrared (NIR) as a function of the relative bias currents and the substrate temperature. We established a physical model based on a 1D electrothermal model to describe the hotspot evolution and thermal diffusion process after a single photon irradiated the nanowire. The simulations are in good agreement with the experimental results and reveal the other influencing factors and potential ways to further improve the timing jitter of SNSPDs. Finally, we introduce a new time-resolved approach, where by collecting the instrument response function (IRF) of SNSPDs, the wavelength of the incident photons can be easily discriminated with a resolution below 80 nm.