  In this work, we have studied the logarithmic entropy corrected holographic
dark energy (LECHDE) model with Granda-Oliveros (G-O) IR cutoff. The evolution
of dark energy (DE) density $\Omega'_D$, the deceleration parameter, $q$, and
equation of state parameter (EoS), $\omega_{\Lambda}$, are calculated. We show
that the phantom divide may be crossed by choosing proper model parameters,
even in absence of any interaction between dark energy and dark matter. By
studying the statefinder diagnostic and
$\omega_{\Lambda}-\omega_{\Lambda}^{\prime}$ analysis, the pair parameters
$\{r,s\}$ and $(\omega_{\Lambda}-\omega_{\Lambda}^{\prime})$ is calculated for
flat GO-LECHDE universe. At present time, the pair $\{r,s\}$ can mimic the
$\Lambda$CDM scenario for a value of $\alpha/\beta\simeq 0.87$, which is lower
than the corresponding one for observational data ($\alpha/\beta=1.76$) and for
Ricci scale ($\alpha/\beta=2$). We find that at present, by taking the various
values of ($\alpha/\beta$), the different points in $r-s$ and
$(\omega_{\Lambda}-\omega_{\Lambda}^{\prime})$ plans are given. Moreover, in
the limiting case for a flat dark dominated universe at infinity ($t\rightarrow
\infty$), we calculate $\{r,s\}$ at G-O scale. For Ricci scale ($\alpha = 2$,
$\beta = 1$) we obtain $\{r=0,s=2/3\}$.
