The extraordinary magnetic Ap star HD 75049 has been studied with data obtained with the European Southern Observatory Very Large Telescope and 2.2-m telescopes. Direct measurements reveal that the magnetic field modulus at maximum reaches 30 kG. The star shows photometric, spectral and magnetic variability with a rotation period of 4.049 d. Variations of the mean longitudinal magnetic field can be described to first order by a centred dipole model with an inclination i = 25 degrees, an obliquity beta = 60 degrees and a polar field B(p) = 42 kG. The combination of the longitudinal and surface magnetic field measurements implies a radius of R = 1.7 R(circle dot), suggesting that the star is close to the zero-age main sequence. HD 75049 displays moderate overabundances of Si, Ti, Cr, Fe and large overabundances of rare earth elements. This star has the second strongest magnetic field of any main-sequence star after Babcock's star, HD 215441, which it rivals.