The author introduces multiple \(p\)-adic log-gamma functions defined on \(\mathbb C_p\setminus\mathbb Z_p\) for nonnegative integers, which are generalizations of Diamond's \(p\)-adic log--gamma function, and give properties characterizing them. More precisely, for nonnegative integers \(r\), multiple \(p\)-adic log-gamma functions \(\text{Log}\,\Gamma_{D,r}(x)\) are defined by \[ \text{Log}\,\Gamma_{D,r}(x)= \begin{cases} \int_{\mathbb Z^r_p} \varphi_r(x+ t_1+\cdots+ t_r)\,dt_1\cdots dt_r\quad &\text{if }r\geq 1,\qquad\text{and}\\ \log_p(x)\quad &\text{if }r= 0\end{cases} \] for \(x\in\mathbb C_p\setminus\mathbb Z_p\), where \(\varphi_r(x)\) is the function defined by Endo as \[ \varphi_r(x)= \begin{cases} {x^r\over r!}\,(\log_px- \sum^r_{i=1} {1\over i})\quad &\text{for }r\geq 1,\qquad\text{and}\\ \log_p x\quad &\text{for }r= 0.\end{cases} \] Then the main theorem of the paper is the following: Theorem. (1) For a positive integer \(r\) and \(x\in\mathbb C\setminus\mathbb Z_p\), \[ r\int_{\mathbb Z_p} \text{Log\,}\Gamma_{D,r}(x+ t)\,dt= (x- r)(\text{Log\,}\Gamma_{D, r})'(x)- S_r(x), \] where \(S_r(x)= {1\over r!} \int_{\mathbb Z^r_p} (x+ t_1+\cdots+ t_r)^r\,dt_1\cdots dt_r\) is the multiple Bernoulli polynomial. (2) For a positive integer \(r\), \(\text{Log}\,\Gamma_{D,r}(x)\) is the unique strictly differentiable function \(f: \mathbb C_p\setminus\mathbb Z)p\to \mathbb C_p\) satisfying the conditions \[ \begin{aligned} (\text{A})\qquad f(x+ 1)- f(x) &= \text{Log\,}\Gamma_{D,r-1}(x),\qquad\text{and}\\ (\text{B}\qquad r\int_{\mathbb Z_p} f(x+ t)\,dt &= (x- r)f'(x)- S_r(x).\end{aligned} \] In the final section, the author introduces multiple \(p\)-adic log-gamma functions \(\text{Log\,}\Gamma_{M,r}(x)\) defined on \(\mathbb Z_p\), and shows that this function also satisfies the similar equation to (B) in the main theorem.