  In this work we explore the possible evolutionary track of the neutron star
in the newly discovered Be/X-ray binary SXP 1062, which is believed to be the
first X-ray pulsar associated with a supernova remnant. Although no cyclotron
feature has been detected to indicate the strength of the neutron star's
magnetic field, we show that it may be $\ga 10^{14} $G. If so SXP 1062 may
belong to the accreting magnetars in binary systems. We attempt to reconcile
the short age and long spin period of the pulsar taking account of different
initial parameters and spin-down mechanisms of the neutron star. Our calculated
results show that, to spin down to a period $\sim 1000 $s within $10-40 $kyr
requires efficient propeller mechanisms. In particular, the model for angular
momentum loss under energy conservation seems to be ruled out.
