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A thermonuclear explosion triggered by a He-shell detonation on a carbonâ€"oxygen white-dwarf core has been predicted to have strong UV line blanketing at early times due to the iron-group elements produced during He-shell burning. We present the photometric and spectroscopic observations of SN 2016dsg, a subluminous peculiar Type I supernova consistent with a thermonuclear explosion involving a thick He shell. With a redshift of 0.04, the i -band peak absolute magnitude is derived to be around âˆ'17.5. The object is located far away from its host, an early-type galaxy, suggesting it originated from an old stellar population. The spectra collected after the peak are unusually red, show strong UV line blanketing and weak O i λ 7773 absorption lines, and do not evolve significantly over 30 days. An absorption line around 9700â€"10500 Ă... is detected in the near-infrared spectrum and is likely from the unburnt He in the ejecta. The spectroscopic evolution is consistent with the thermonuclear explosion models for a sub-Chandrasekhar-mass white dwarf with a thick He shell, while the photometric evolution is not well described by existing models. [ABSTRACT FROM AUTHOR]