We report results for the X-ray spectrum of a millisecond pulsar, PSR J2124
-3358 observed with ASCA. This pulsar is an isolated 4.9 ms pulsar (Bailes
et al 1997). Its X-ray pulsation was detected with ROSAT HRI in the 0.1- 2.
4 keV band(Becker & Trumper 1998). The pulse profile was broad, and there i
s an indication of a secondary peak. Due to the lack of spectral informatio
n, the nature of the S-ray emission was unclear. An ASCA observation of thi
s pulsar was carried out in May 1998, and provided the X-ray spectrum in th
e energy band from 0.5 to 10.0 keV. Due to poor statistics, the X-ray pulsa
tion was not confirmed by ASCA.