  The intermediate-mass binary pulsars (IMBPs) are characterized by relatively
long spin periods (10 - 200 ms) and massive ($\ga 0.4 M_{\odot}$) white dwarf
(WD) companions. Recently, precise mass measurements have been performed for
the pulsar and the WD in the IMBP PSR J1802-2124. Some observed properties,
such as the low mass of the pulsar, the high mass of the WD, the moderately
long spin period, and the tight orbit, imply that this system has undergone a
peculiar formation mechanism. In this work, we attempt to simulate the detailed
evolutionary history of PSR J1802-2124. We propose that a binary system
consisting of a neutron star (NS, of mass $1.3 M_{\odot}$) and an He star (of
mass $1.0 M_{\odot}$), and with an initial orbital period of 0.5 d, may have
been the progenitor of PSR J1802-2124. Once the He star overflows its Roche
lobe, He-rich material is transferred onto the NS at a relatively high rate of
$\sim 10^{-7}-10^{-6} M_{\odot}\,\rm yr^{-1}$, which is significantly higher
than the Eddington accretion rate. A large amount of the transferred material
is ejected from the vicinity of the NS by radiation pressure and results in the
birth of a mildly recycled pulsar. Our simulated results are consistent with
the observed parameters of PSR J1802-2124. Therefore, we argue that the NS + He
star evolutionary channel may be responsible for the formation of most IMBPs
with orbital periods $\la 3 \rm d$.
