Aims: We aim to interpret the photometric and spectroscopic variability of the luminous blue variable supergiant HD 50064 (V = 8.21). Methods: CoRoT space photometry and follow-up high-resolution spectroscopy with a time base of 137 d and 169 d, respectively, was gathered, analysed, and interpreted using standard time series analysis and light curve modelling methods, as well as spectral line diagnostics. Results: The space photometry reveals one period of 37 d, which undergoes a sudden amplitude change with a factor 1.6. The pulsation period is confirmed in the spectroscopy, which additionally reveals metal line radial velocity values differing by 30 km s-1 depending on the spectral line and on the epoch. We estimate Teff 13 500 K, log g 1.5 from the equivalent width of Si lines. The Balmer lines reveal that the star undergoes episodes of changing mass loss on a time scale similar to the changes in the photometric and spectroscopic variability, with an average value of log dot{M} ≃ -5 (in M_⊙ yr-1). We tentatively interpret the 37 d period as the result of a strange mode oscillation. Based on high-resolution spectroscopy assembled with the CORALIE spectrograph attached to the 1.2 m Euler telescope at La Silla, Chile and on CoRoT space-based photometry. The CoRoT space mission was developed and is operated by the French space agency CNES, with the participation of ESA's RSSD and Science Programmes, Austria, Belgium, Brazil, Germany, and Spain.Postdoctoral Fellow of the Fund for Scientific Research of Flanders (FWO), Belgium.