A weighted version of the geometric mean of k ($geq;3$) positive invertible operators is given. For operators $A_1,{ldots},A_k$ and for nonnegative numbers ${alpha}_1,ldots,{alpha}_k$ such that $sum_limits_{i=1}^k;alpha_i=1$, we define weighted geometric means of two types, the first type by a direct construction through symmetrization procedure, and the second type by an indirect construction through the non-weighted (or uniformly weighted) geometric mean. Both of them reduce to $A_1^{alpha_1}{cdots}A_k^{{alpha}_k}$ if $A_1,{ldots},A_k$ commute with each other. The first type does not have the property of permutation invariance, but satisfies a weaker one with respect to permutation invariance. The second type has the property of permutation invariance. We also show a reverse inequality for the arithmetic-geometric mean inequality of the weighted version.