  Long term observations by Brook et al. reveal that the derivative of
rotational frequency of PSR J0738-4042 changed abruptly in 2005. Originally,
the spin-down rate was relatively stable, with the rotational frequency
derivative of $-1.14 \times 10^{-14}~\rm s^{-2}$. After September 2005, the
derivative began to rise up. About 1000 days later, it arrived at another
relatively stable value of about $-0.98 \times 10^{-14}~\rm s^{-2}$, indicating
that the pulsar is spinning-down relatively slowly. To explain the observed
spin-down rate change, we resort to an asteroid disrupted by PSR J0738-4042. In
our model, the orbital angular momentum of the asteroid is assumed to be
parallel to that of the rotating pulsar, so that the pronounced reduction in
the spin-down rate can be naturally explained as due to the transfer of the
angular momentum from the disrupted material to the central pulsar. The derived
magnetospheric radius is about $4.0 \times 10^{9}$ cm, which is smaller than
the tidal disruption radius ($4.9 \times 10^{10}$ cm). Our model is
self-consistent. It is shown that the variability of the spin-down rate of PSR
J0738-4042 can be quantitatively accounted for by the accretion from the
asteroid disrupted by the central pulsar.
