  Rapid sky localization of gravitational wave sources is crucial to enable
prompt electromagnetic follow-ups. In this article, we present a novel
semianalytical approach for sky localization of gravitational waves from
compact binary coalescences. We use the Bayesian framework with an analytical
approximation to the prior distributions for a given astrophysical model. We
derive a semianalytical solution to the posterior distribution of source
directions. This method only requires one-fold numerical integral that
marginalizes over the merger time, compared to the five-fold numerical
integration otherwise needed in the Bayesian localization method. The
performance of the method is demonstrated using a set of binary neutron stars
(BNS) injections on Gaussian noise using LIGO-Virgo's design and O2
sensitivity. We find the median of 90% confidence area in O2 sensitivity to be
$\mathcal{O}(10^2) ~\mathrm{deg}^2$, comparable to that of the existing
LIGO-Virgo online localization method Bayestar and parameter estimation toolkit
LALInference. In the end, we apply this method to localize the BNS event
GW170817 and find the 50% (90%) confidence region of 11 $\mathrm{deg}^2$ (50
$\mathrm{deg}^2$). The detected optical counterpart of GW170817 resides within
our 50% confidence area.
