We can construct an Iitaka fibration for every $\mathbb{Q}$-Cartier divisor $D$ on a normal projective variety such that the Iitaka dimension of $D$ is nonnegative. More precisely, the linear system of $mD$ defines the Iitaka fibration for some positive integer $m$. The effectivity of Iitaka fibration is a topic to study what $m$ depends on under some conditions of $D$. In this talk, I will introduce a result on the effectivity of Iitaka fibration for $D$ such that $D$ is the sum of the log canonical divisor of an lc pair and an ample divisor. This is a work in progress.