Aims. The magnetic field of accreting neutron stars determines their overall behavior including the maximum possible luminosity. Some models require an above-average magnetic field strength (≳1013 G) in order to explain super-Eddington mass accretion rate in the recently discovered class of pulsating ultraluminous X-ray sources (ULX). The peak luminosity of SMC X-3 during its major outburst in 2016–2017 reached ~2.5 × 1039 erg s-1 comparable to that in ULXs thus making this source the nearest ULX-pulsar. Determination of the magnetic field of SMC X-3 is the main goal of this paper. Methods. SMC X-3 belongs to the class of transient X-ray pulsars with Be optical companions, and exhibited a giant outburst in July 2016–March 2017. The source has been observed over the entire outburst with the Swift/XRT and Fermi/GBM telescopes, as well as the NuSTAR observatory. Collected data allowed us to estimate the magnetic field strength of the neutron star in SMC X-3 using several independent methods. Results. Spin evolution of the source during and between the outbursts, and the luminosity of the transition to the so-called propeller regime in the range of (0.3–7) × 1035 erg s-1 imply a relatively weak dipole field of (1–5) × 1012 G. On the other hand, there is also evidence for a much stronger field in the immediate vicinity of the neutron star surface. In particular, transition from super- to sub-critical accretion regime associated with the cease of the accretion column and very high peak luminosity favor a field that is an order of magnitude stronger. This discrepancy makes SMC X-3 a good candidate for possessing significant non-dipolar components of the field, and an intermediate source between classical X-ray pulsars and accreting magnetars which may constitute an appreciable fraction of ULX population.