The Be X-ray pulsar ( BeXRP ) SXP 59 underwent a giant outburst in 2017 with a peak X-ray luminosity of 1.1 \times 10 ^ { 38 } erg s ^ { -1 } . We report on the X-ray behaviour of SXP 59 with the XMM–Newton and NuSTAR observations collected at the outburst peak , decay , and the low luminosity states . The pulse profiles are energy dependent , the pulse fraction increases with the photon energy and saturates at \sim 65 % above 10 keV . It is difficult to constrain the change in the geometry of emitting region with the limited data . Nevertheless , because the pulse shape generally has a double-peaked profile at high luminosity and a single peak profile at low luminosity , we prefer the scenario that the source transited from the super-critical state to the sub-critical regime . This result would further imply that the neutron star ( NS ) in SXP 59 has a typical magnetic field . We confirm that the soft excess revealed below 2 keV is dominated by a cool thermal component . On the other hand , the NuSTAR spectra can be described as a combination of the non-thermal component from the accretion column , a hot blackbody emission , and an iron emission line . The temperature of the hot thermal component decreases with time , while its size remains constant ( R \sim 0.6 km ) . The existence of the hot blackbody at high luminosity can not be explained with the present accretion theories for BeXRPs . It means that either more sophisticated spectral models are required to describe the X-ray spectra of luminous BeXRPs , or there is non-dipole magnetic field close to the NS surface .