As a radio-loud narrow-line Seyfert 1 galaxy (NLS1) detected by Fermi/LAT in GeV $gamma$-rays, 1H 0323+342 is a remarkable Active Galactic Nucleus (AGN) showing properties characteristic of both NLS1s and blazars. Here we present results of simultaneous X-ray and UV/optical monitoring observations on 1H 0323+342 taken with the UV/Optical Telescope (UVOT) and X-ray Telescope (XRT) onboard the Swift satellite over six years from 2006. Overall, the object showed statistically correlated variations in both the UV and X-ray bands on timescales of years as well as on timescales of days. A deep Suzaku observation reveals X-ray variability on timescales as short as a few tens of thousand seconds, and an X-ray spectrum typical of Seyfert galaxies. The broad-band spectral energy distribution, for which the data of UV and X-ray observations taken on 2009 July 26-27 were used, can be well modeled with a simple one-zone leptonic jet model plus accretion disk/corona emission. The latter is predominantly responsible for the UV/optical and X-ray (0.3-10 keV) emission and their observed variations. The correlated UV-X-ray variability on the timescale of days is consistent with reprocessing of the X-ray radiation by the accretion disk. The shortest timescale and large normalized excess variance of the X-ray variability detected with Suzaku suggest a relatively small black hole mass of the order of $10^7M_{odot}$, consistent with the estimation based on the broad H$beta$ line in the optical.