We use the observational data in radio, optical and X-ray wavebands, for a sample of active galactic nuclei (AGNs) with measured black hole masses, to explore the origin of radio emission from nearby low-luminosity active galactic nuclei (LLAGNs). We find that the radio luminosities are higher than the maximal luminosities expected from the ADAF model, for most sources in this sample. This implies that the radio emission is dominantly from the jets in these sources. The radio emission from a small fraction of the sources in this sample can be explained by the ADAF model. However, comparing the observed multi-band emission data with the spectra calculated for the ADAF or ADIOS cases, we find that neither ADAF nor ADIOS models can reproduce the observed multi-band emission simultaneously, with reasonable magnetic field strengths, for these radio-weak sources. A variety of other possibilities are discussed, and we suggest that the radio emission is probably dominated by jet emission even in these radio-weak LLAGNs.

25 pages, some references were added, accepted for publication in ApJ