In this paper, we study the case of independent sums in multi-risk model. Assume that there exist $k$ types of variables. The $i$th are denoted by $\{X_{ij},j\geq1\}$, which are i.i.d. with common density function $f_i(x)\in\mathcal {OR}$ and finite mean, $i=1,\ldots,k$. We investigate local large deviations for partial sums $\sum_{i=1}^{k}S_{n_{i}}=\sum_{i=1}^{k}\sum_{j=1}^{n_{i}}X_{ij}$.
