Quite recently, Alotaibi and Mohiuddine (Adv. Differ. Equ. 2012:39, 2012) studied the idea of a random 2-normed space to determine some stability results concerning the cubic functional equation. In this paper, we define and study the concepts of I-convergence and I * -convergence for double sequences in random 2-normed spaces and establish the relationship between these types of convergence, i.e. ,w e show that I * -convergence implies I-convergence in random 2-normed spaces. Furthermore, we have also demonstrated through an example that, in general, I-convergence does not imply I * -convergence in random 2-normed spaces. MSC: 40A05; 46A70