We present DES14X2fna, a high-luminosity, fast-declining Type IIb supernova (SN IIb) at redshift z = 0.0453, detected by the Dark Energy Survey (DES). DES14X2fna is an unusual member of its class, with a light curve showing a broad, luminous peak reaching Mr ≃ −19.3 mag 20 d after explosion. This object does not show a linear decline tail in the light curve until ≃60 d after explosion, after which it declines very rapidly (4.30 ± 0.10 mag 100 d−1 in the r band). By fitting semi-analytic models to the photometry of DES14X2fna, we find that its light curve cannot be explained by a standard 56Ni decay model as this is unable to fit the peak and fast tail decline observed. Inclusion of either interaction with surrounding circumstellar material or a rapidly-rotating neutron star (magnetar) significantly increases the quality of the model fit. We also investigate the possibility for an object similar to DES14X2fna to act as a contaminant in photometric samples of SNe Ia for cosmology, finding that a similar simulated object is misclassified by a recurrent neural network (RNN)-based photometric classifier as an SN Ia in ∼1.1–2.4 per cent of cases in DES, depending on the probability threshold used for a positive classification.