In this paper, we investigate approximations of the inverse moment model by widely orthant dependent (WOD) random variables. Let $\{Z_{n},n\geq1\}$ be a sequence of nonnegative WOD random variables, and $\{w_{ni},1\leq i\leq n,n\geq 1\}$ be a triangular array of nonnegative nonrandom weights. If the first moment is finite, then $E(a+ \sum_{i=1}^{n}w_{ni}Z_{i})^{-\alpha}\sim (a+\sum_{i=1}^{n}w_{ni}EZ_{i})^{-\alpha}$ for all constants $a>0$ and $\alpha>0$ . If the rth moment ( $r>2$ ) is finite, then the convergence rate is presented as $\frac{E(a+\sum_{i=1}^{n}w_{ni}Z_{i})^{-\alpha}}{(a+\sum_{i=1}^{n}w_{ni}EZ_{i})^{-\alpha}}-1=O(\frac{1}{(a+\sum_{i=1}^{n}w_{ni}EZ_{i})^{1-2\beta/r}})$ , where $\beta\geq0$ and $2\beta/r<1$ . Finally, some simulations illustrate the results. We generalize some corresponding results.