Aims: Most hot Jupiters are expected to spiral in toward their host stars because the angular momentum of the orbital motion is transferred to the stellar spin. Their orbits can also precess as a result of planet-star interactions. Calculations show that both effects might be detected for the very-hot exoplanet WASP-12 b using the method of precise transit-timing over a time span of about 10 yr. Methods: We acquired new precise light curves for 29 transits of WASP-12 b, spannning four observing seasons from November 2012 to February 2016. New mid-transit times, together with those from the literature, were used to refine the transit ephemeris and analyze the timing residuals. Results: We find that the transit times of WASP-12 b do not follow a linear ephemeris with a 5σ confidence level. They may be approximated with a quadratic ephemeris that gives a change rate in the orbital period of (-2.56 ± 0.40) × 10-2 s yr-1. The tidal quality parameter of the host star was found to be equal to 2.5 × 105, which is similar to theoretical predictions for Sun-like stars. We also considered a model in which the observed timing residuals are interpreted as a result of the apsidal precession. We find, however, that this model is statistically less probable than the orbital decay. Partly based on (1) data collected with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, (2) observations made at the Centro Astronómico Hispano Alemán (CAHA), operated jointly by the Max-Planck Institut für Astronomie and the Instituto de Astrofísica de Andalucía (CSIC), and (3) data collected with telescopes at the Rozhen National Astronomical Observatory.The light curves are available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/588/L6