In this paper, we approximate common fixed points of two asymptotically nonexpansive mappings in the intermediate sense by three-step iteration process with random errors. Our weak and strong convergence results extend, generalize and improve the corresponding results of Kim and Kim in 2001, Kim, Kiuchi and Takahashi in 2004, Khan and Takahashi in 2000, Rhoades in 1994, Tan and Xu in 1993, and Xu and Noor in 2002.