Multispectral imaging through scattering media is an important practical issue in the field of sensing. The light from a scattering medium is expected to carry information about the spectral properties of the medium, as well as geometrical information. Because spatial and spectral information of the object is encoded in speckle images, the information about the structure and spectrum of the object behind the scattering medium can be estimated from those images. Here we propose a deep learning-based strategy that can estimate the central wavelength from speckle images captured with a monochrome camera. When objects behind scattering media are illuminated with narrowband light having different spectra with different spectral peaks, deep learning of speckle images acquired at different central wavelengths can extend the spectral region to reconstruct images and estimate the central wavelengths of the illumination light. The proposed method achieves central wavelength estimation in 1 nm steps for objects whose central wavelength varies in a range of 100 nm. Because our method can achieve image reconstruction and central wavelength estimation in a single shot using a monochrome camera, this technique will pave the way for multispectral imaging through scattering media.