  The fastest millisecond pulsar PSR B1937+21 presents an interpulse separated
from the main pulse by nealy 180^o at radio frequencies. Recently, the ASCA
observations (Takahashi et al. 2001) detected pulsed X-ray emission from this
pulsar. Only a single narrow X-ray pulse is observed, which is coincident with
the radio interpulse in phase. We investigate the possible origin of the pulsed
X-rays from the polar cap (PC) accelerators or the outer gap (OG) accelerators
in the frame of PC model and OG model, respectively, by assuming a dipolar
magnetic field structure and the same radio emission pattern from its poles for
the pulsar. The OG model can naturally explain the main observational facts.
For the PC model, the coincidence between the X-ray pulse and the radio
interpulse can not be reproduced in the assumed case. However when considering
possible deviation from our assumption, PC model may still be valid for this
pulsar in some cases.
