  We study the mid-infrared (IR) and near-ultraviolet (UV) excess emissions of
spectroscopically selected quiescent galaxies on the optical red sequence. We
use the Wide-field Infrared Survey Explorer ({\it WISE}) mid-IR and Galaxy
Evolution Explorer ({\it GALEX}) near-UV data for a spectroscopic sample of
galaxies in the Sloan Digital Sky Survey Data Release 7 to study the possible
connection between quiescent red-sequence galaxies with and without
mid-IR/near-UV excess. Among 648 12 $\mu$m detected quiescent red-sequence
galaxies without H$\alpha$ emission, 26% and 55% show near-UV and mid-IR excess
emissions, respectively. When we consider only bright ($M_{r}$ $<$ $-$21.5)
galaxies with early-type morphology, the fraction of galaxies with recent star
formation is still 39%. The quiescent red-sequence galaxies with mid-IR and
near-UV excess emissions are optically fainter and have slightly smaller
$D_{n}$4000 than those without mid-IR and near-UV excess emissions. We also
find that mid-IR weighted mean stellar ages of quiescent red-sequence galaxies
with mid-IR excess are larger than those with near-UV excess, and smaller than
those without mid-IR and near-UV excess. The environmental dependence of the
fraction of quiescent red-sequence galaxies with mid-IR and near-UV excess
seems strong even though the trends of quiescent red-sequence galaxies with
near-UV excess differ from those with mid-IR excess. These results indicate
that the recent star formation traced by near-UV ($\lesssim 1$ Gyr) and mid-IR
($\lesssim 2$ Gyr) excess is not negligible among nearby, quiescent, red,
early-type galaxies. We suggest a possible evolutionary scenario of quiescent
red-sequence galaxies from quiescent red-sequence galaxies with near-UV excess
to those with mid-IR excess to those without near-UV and mid-IR excess.
