  In this work, we interpreted the high braking index of PSR J1640$-$4631 with
a combination of the magneto-dipole radiation and dipole magnetic field decay
models. By introducing a mean rotation energy conversion coefficient
$\overline{\zeta}$, the ratio of the total high-energy photon energy to the
total rotation energy loss in the whole life of the pulsar, and combining the
pulsar's high-energy and timing observations with reliable nuclear equation of
state, we estimate the pulsar's initial spin period, $P_{0}\sim (17-44)$ ms,
corresponding to the moment of inertia $I\sim (0.8-2.1)\times 10^{45}$ g
cm$^{2}$. Assuming that PSR J1640$-$4631 has experienced a long-term
exponential decay of the dipole magnetic field, we calculate the true age
$t_{\rm age}$, the effective magnetic field decay timescale $\tau_{D}$, and the
initial surface dipole magnetic field at the pole $B_{p}(0)$ of the pulsar to
be $(2900-3100)$ yrs, $1.07(2)\times10^{5}$ yrs, and $(1.84-4.20)\times10^{13}$
G, respectively. The measured braking index of $n=3.15(3)$ for PSR J1640$-$4631
is attributed to its long-term dipole magnetic field decay and a low magnetic
field decay rate, $dB_{\rm p}/dt\sim -(1.66-3.85)\times10^{8}$ G yr$^{-1}$. Our
model can be applied to both the high braking index ($n>3$) and low braking
index ($n<3$) pulsars, tested by the future polarization, timing, and
high-energy observations of PSR J1640$-$4631.
