  Recent timing observation constrained the braking index of the X-ray pulsar
PSR J1640-4631 to be $n=3.15\pm0.03$, which is the highest value of all pulsars
with measured braking indices so far. In this Letter, we investigate whether
pulsar braking by combined between the magnetic dipole emission and the
gravitational radiation might have a braking index greater than three. For
conventional neutron star and low mass quark star candidates, the inferred
ellipticities derived by the observed braking index are obviously much larger
than the theoretical estimated maximum value. If PSR J1640-4631 is a low-mass
neutron star with a mass of $0.1~ \rm M_{\odot}$, the inferred ellipticity can
be approximately equal to the theoretical estimated maximum value. Because of
the radio-quiet nature of this source, we employ the vacuum gap model developed
by Ruderman and Sutherland to constrain the inclination angle to be
$87.2-90^{\circ}$. Based on this, we propose that a low-mass neutron star with
a large inclination angle can interpret the high braking index and the
radio-quiet nature of this source. Future observations such as gravitational
wave detection and long-term timing for this source are required to confirm or
confute our scenario.
