  We present our optical observations and multi-wavelength analysis of the
GRB\,200613A detected by \texttt{Fermi} satellite. Time-resolved spectral
analysis of the prompt $\gamma$-ray emission was conducted utilizing the
Bayesian block method to determine statistically optimal time bins. Based on
the Bayesian Information Criterion (BIC), the data generally favor the
Band+Blackbody (short as BB) model. We speculate that the main Band component
comes from the Blandford-Znajek mechanism, while the additional BB component
comes from the neutrino annihilation process. The BB component becomes
significant for a low-spin, high-accretion rate black hole central engine, as
evidenced by our model comparison with the data. The afterglow light curve
exhibits typical power-law decay, and its behavior can be explained by the
collision between the ejecta and constant interstellar medium (ISM). Model
fitting yields the following parameters: $E_{K,iso} =
(2.04^{+11.8}_{-1.50})\times 10^{53}$ erg, $\Gamma_0=354^{+578}_{-217}$,
$p=2.09^{+0.02}_{-0.03}$, $n_{18}=(2.04^{+9.71}_{-1.87})\times 10^{2}$
cm$^{-3}$, $\theta_j=24.0^{+6.50}_{-5.54}$ degree,
$\epsilon_e=1.66^{+4.09}_{-1.39})\times 10^{-1}$ and
$\epsilon_B=(7.76^{+48.5}_{-5.9})\times 10^{-6}$. In addition, we employed the
public Python package \texttt{Prospector} perform a spectral energy
distribution (SED) modeling of the host galaxy. The results suggest that the
host galaxy is a massive galaxy ($\log(M_\ast /
M_\odot)=11.75^{+0.10}_{-0.09}$) with moderate star formation rate
($\mbox{SFR}=22.58^{+13.63}_{-7.22} M_{\odot}$/yr). This SFR is consistent with
the SFR of $\sim 34.2 M_{\odot}$ yr$^{-1}$ derived from the [OII] emission line
in the observed spectrum.
