  Low-luminosity AGNs (LLAGNs) are a very important class of sources since they
occupy a significant fraction of local galaxies. Their spectra differ
significantly from the canonical luminous AGNs, most notably by the absence of
the ``big blue bump''. In the present paper, taking a typical
LLAGN--NGC4258--as an example, we investigate the origin of their spectral
emission. The observational data of NGC4258 is extremely abundant, including
water maser emission, putting very strict constraints to its theoretical
models. The infrared (IR) spectrum is well described by a steep power-law form
$f_{\nu}\propto \nu^{-1.4}$, and may extend to the optical/UV band. Up until
now there is no model which can explain such a steep spectrum, and we here
propose a coupled jet plus accretion disk model for NGC4258. The accretion disk
is composed of an inner ADAF (or radiatively inefficient accretion flow) and an
outer standard thin disk. A shock occurs when the accretion flow is ejected out
of the ADAF to form the jet near the black hole, accelerating the electrons
into a power-law energy distribution. The synchrotron and self-Comptonized
emission from these electrons greatly dominates over the underlying accretion
disk and can well explain the spectrum ranging from IR to X-ray bands. The
further propagation of the shocked gas in the jet can explain the flat radio
spectrum of NGC4258. Several predictions of our model are presented for testing
against future observations, and we briefly discuss the application of the
model to other LLAGNs.
