The macroscopic deformed potential energy for super-heavy elements Z = 120 is determined within a generalized liquid drop model (GLDM). The shell correction is calculated with the Strutinsky method and the microscopic single particle energies are derived from the shell model in an axially deformed Woods–Saxon potential with the same quasi-molecular shape. The total potential energy of a nucleus is calculated by the macro-microscopic method as the summation of the liquid-drop energy and the Strutinsky shell correction. The theory is adopted to describe the deformed potential energies in a set of cold reactions. The neck in the quasi-molecular shape is responsible to the deep valley of the fusion barrier due to shell corrections. In the cold fusion path, the double-hump fusion barrier is predicted by the shell correction and complete fusion events may occur. The results show that some of projectile–target combinations in the entrance channel, such as ⁵⁰Ca+²⁵²Fm→ ³⁰²120* and ⁵⁸Fe+²⁴⁴Pu→ ³⁰²120*, favour the fusion reaction, which can be considered as candidates for the synthesis of super heavy nuclei Z = 120 and the former might be the best cold fusion reaction to produce the nucleus ³⁰²120 among them.