Quantum computers are the promising candidates for simulation of large quantum systems, which is a daunting task to perform in a classical computer. Here we report the experimental realization of quantum tunneling of a single particle through different types of potential barriers by simulating it in the IBM quantum computer, which here acts as a universal quantum simulator. We consider two-qubit and three-qubit systems for visualizing the tunneling process illustrating its unique quantum nature. We clearly observe the tunneling and oscillations of the particles in a step potential and in double-and multi-well potentials through our experimental results. The proposed quantum circuits and simulational techniques used here can be extended for observing the tunneling phenomena for multi-particle systems in different shaped potentials.