This paper presents a study on Topology optimization of continuum structures with the aim of maximizing the lowest buckling load factor. In the structural shape and topology optimization problems, stability and buckling issues are not usually considered therefore in some cases, long and thin members are obtained in an optimized configuration that can lead to the instability of the structure. In this article level set method incorporating a fictitious interface, energy is applied to find the optimal configuration. One of the main problems in traditional continuum structural optimization methods, which are based on the removal or alterations in element density, is the creation of pseudo buckling modes in the optimization process. These pseudo buckling modes should be identified and removed. The level set optimization method, which is grounded on moving the structure's boundary, has a high ability to control topological complexities. Therefore, the idea of using the level set method has led to the elimination of pseudo buckling modes and the resolving of this problem. Derivation of the required speed term in the level set method is complicated and this derivation term for the buckling load factor is the innovation of this research. Numerical examples are illustrated to prove the effectiveness of this method.