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In this paper, we consider the continuous parabolic Anderson model (PAM)driven by a time-independent log-correlated Gaussian field (LGF). We obtain anasymptotic result of  $$\mathbb{E}\exp\Bigg\{\frac{1}{2}\sum\limits_{j,k=1}^N\int_0^t\int_0^t\gamma(B_j(s)-B_k(r))drds\Bigg\}\qquad(N\rightarrow  \infty)$$ which is composed of the independent Brownian motions $\{B_j(s)\}$and the function $\gamma$ approximating to a logarithmic potential at $0$, suchas the covariances of massive free field and Bessel field. Based on theasymptotic result, we get the precise high moment asymptotics for Feynman-Kacformula of the PAM with LGF.

Precise high moment asymptotics for parabolic Anderson model with log-correlated Gaussian field