We report the analysis of a highly magnetized neutron star in the Large Magellanic Cloud (LMC). The high-mass X-ray binary pulsar Swift J045106.8-694803 has been observed with Swift X-ray telescope (XRT) in 2008, the Rossi X-ray Timing Explorer (RXTE) in 2011 and the X-ray Multi-Mirror Mission-Newton (XMM-Newton) in 2012. The change in spin period over these four years indicates a spin-up rate of -5.01 ± 0.06 s yr-1, amongst the highest observed for an accreting pulsar. This spin-up rate can be accounted for using Ghosh & Lamb accretion theory assuming it has a magnetic field of (1.2 ± 0.20.7) × 1014 G. This is over the quantum critical field value. There are very few accreting pulsars with such high surface magnetic fields and this is the first of which to be discovered in the LMC. The large spin-up rate is consistent with Swift Burst Alert Telescope (BAT) observations which show that Swift J045106.8-694803 has had a consistently high X-ray luminosity for at least five years. Optical spectra have been used to classify the optical counterpart of Swift J045106.8-694803 as a B0-1 III-V star and a possible orbital period of 21.631 ± 0.005 d has been found from Massive Compact Halo Object (MACHO) optical photometry.