The investigation of the strong interactions in hadronic atoms is the main motivation to study the exotic atoms. For this purpose a negetive charge particle which can be a meson or a baryon, enters a target then atomic electron is replaced by the particle and finally a highly exited hadronic atom is formed. The particle then cascade down to atomic levels and it interacts strongly with the nucleus, and eventually is absorbed by the nucleus. One of these kind atoms which is important both theoretically and experimentally, is formed by mesons including strangeness like kaon ( K - ). Density dependent optical potential improved by Friedman can describe the interaction between kaon and nucleus, correctly. So we have solved the Klein-Gordon equation by this potential and Numerov method. Interaction between kaon and 118 Sn as a heavy nucleus has been studied. The atomic states of this system were calculated and campared with the experimental data. The bound nuclear states were also be determined. For this purpose, we have used two-parameter Fermi function for nuclear density. Then the K - 40 Ca system studied . U sing a two-parameter Fermi function for nuclear density, all nuclear levels of this interaction are calculated. Then we investigate the behavior of the K - in medium nucleus of 12 C , using a modified harmonic oscillator model for nuclear density . Calculating three nuclear levels, it was founded that deeply bound nuclear states of kaon can be formed in carbon. The results of this work for calcium and carbon nuclei were compared to the results obtained by other works, and it showed a relatively good consistency. At the end , we studied two-body interaction between kaon and 3 He by this method. To calculate the density of helium-3, we used a model, achieved from the solution of the Schr?dinger equation for a three-body system and we calculated one deeply bound nuclear state for this system. Yamazaki-Akaishi also have calculated one nuclear bound state for this system using a different model. Calculating these levels, we have shown that kaon in light, medium and heavy nuclei, before its decay to main channel, allocates a short time to stay at deeply bound nuclear states. Since these levels have a large width, they will have a very short lifetime and decay to their channel. In fact, these bound states reinforce the idea that kaon-nucleus system, before its decay to main channel, creates quasi bound nuclear states, and if experimental method is improved, it will be expected that these bound states can be observed experimentally.