The spin behaviour of the neutron star in the newly discovered young Be/X-ray long-period pulsar SXP 1062 is discussed. The star is observed to rotate with the period of 1062 s, and spin down at the rate ∼−2.6 × 10−12 Hz s−1. I show that all of the conventional accretion scenarios encounter major difficulties in explaining the rapid spin-down of the pulsar. These difficulties can be, however, avoided within the magnetic accretion scenario in which the neutron star is assumed to accrete from a magnetized wind. The spin-down rate of the pulsar can be explained within this scenario provided the surface magnetic field of the neutron star is B*∼ 4 × 1013 G. I show that the age of the pulsar in this case lies in the range (2–4) × 104 yr, which is consistent with observations. The spin evolution of the pulsar is briefly discussed.