Context: For seven years, the EROS-2 project obtained a mass of photometric data on variable stars. We present a peculiar Cepheid-like star, in the direction of the Small Magellanic Cloud, which demonstrates unusual photometric behaviour over a short time interval. Aims: We report on data of the photometry acquired by the MARLY telescope and spectroscopy from the EFOSC instrument for this star, called EROS2 J005135-714459(sm0060n13842), which resembles the unusual Cepheid HR 7308. Methods: The light curve of our target is analysed using the Analysis of Variance method to determine a pulsational period of 5.5675 days. A fit of time-dependent Fourier coefficients is performed and a search for proper motion is conducted. Results: The light curve exhibits a previously unobserved and spectacular change in both mean magnitude and amplitude, which has no clear theoretical explanation. Our analysis of the spectrum implies a radial velocity of 104 km s-1 and a metallicity of -0.4±0.2 dex. In the direction of right ascension, we measure a proper motion of 17.4±6.0 mas yr-1 using EROS astrometry, which is compatible with data from the NOMAD catalogue. Conclusions: The nature of EROS2 J005135-714459(sm0060n13842) remains unclear. For this star, we may have detected a non-zero proper motion, which would imply that it is a foreground object. Its radial velocity, pulsational characteristics, and photometric data, however, suggest that it is instead a Cepheid-like object located in the SMC. In such a case, it would present a challenge to conventional Cepheid models. Based on observations made by the EROS-2 collaboration with the MARLY, 1.54 m Danish and 3.60 m telescopes at the European Southern Observatory, La Silla, Chile. The photometric data is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/486/891