  In the effective theory of loop quantum cosmology LQC, the influence of the
holonomy correction (with $\overline{\mu}$-scheme) on the homogeneous and the
inhomogeneous cosmological models have been extensively studied in the case of
flat space. In this paper,using the K-Quantization method and the
$\overline{\mu}$-scheme,in the same framework of LQC,we construct the
Hamiltonian constraint operator of the closed FRW model (k=+1), we show that
the effective semi-classical limit gives the same holonomy correction
expression that was already used in the case of a flat space. We also derive
the modified Friedman equation. The numerical investigation is performed to
plot the effective evolution of the massless scalar field in term of the
volume,which indicate a minimum volume at the bounce and also a suitable
infrared behavior.The condition that we apply to constrain the value of
$\overline{\mu}$ in the semi-classical limit is consistent with the numerical
results.
