The study of the seismic vulnerability of existing structures is an important issue. Many researches have been developed in order to investigate the structural behavior of these structures, and extract the basic informations needed to establish retrofitting guidelines in order to reduce the seismic risk to acceptable levels. The most accurate analysis procedure for the structures subjected to strong ground motions is the time-history analysis. This method is time-consuming though for application in all practical purposes. The necessity for faster methods that would ensure a reliable structural assessment or design of structures subjected to seismic loading led to the pushover analysis. Pushover analysis is a non-linear static analysis based on the assumption that structures oscillate predominantly in the first mode or in the lower modes of vibration during a seismic event. The present work deals with seismic vulnerability assessment of an old existing reinforced concrete structure – Perret tower – located in Grenoble, France. After a brief description of the structure in exam, a preliminary computation of the mass of the building and the definition of every existing section are performed. A simplified 3D numerical model is carried out using a finite element code based on multifiber beams approach. Firstly, a non-linear temporal dynamic analysis is performed, then a conventional and adaptive pushover analysis is carried out. The results obtained of the studied cases are then compared: it is observed that the conventional pushover analysis should be adjusted in order to take into account the change of dynamic characteristics due to the formation of plastic mechanisms. Finally, the tower critical levels in term of damage are highlighted.