Structural damage identification (SDI) plays a major role in structural health monitoring (SHM), which has been demanded by researchers to better face the challenges in the aging civil engineering, such as bridge structure and building structure. Many methods have been developed for the application to the real structures, but there are still some difficulties which result in inaccurate, even false damage identification. As a variant of particle swarm optimization (PSO), bare bones particle swarm optimization (BBPSO) is a simple but very powerful optimization tool. However, it is easy to be trapped in the local optimal state like other PSO algorithms, especially in SDI problems. In order to improve its performance in SDI problems, this paper aims to propose a novel optimization algorithm which is named as bare bones particle swarm optimization with double jump (BBPSODJ) for finding a new solution to the SDI problem in SHM field. To begin with, after the introduction of sparse recovery theory, the mathematical model for SDI is established where an objective function based on l1 regularization is constructed. Secondly, according to the basic theory of the BBPSODJ, a double jump strategy based on the BBPSO is designed to enhance the dynamic of particles, and it is able to make a large change in particle searching scopes, which can improve the search behaviour of BBPSO and prevent the algorithm from being trapped into local minimum state. Thirdly, three optimization test functions and a numerical example are utilized to validate the optimization performance of BBPSO, traditional PSO, and genetic algorithm (GA) comparatively; it is obvious that the proposed BBPSODJ shows great self-adapting property and good performance in the optimization process by introducing the novel double jump strategy. Finally, in the laboratory, an experimental example of steel frame with 4 damage cases is implemented to further assess the damage identification capability of the BBPSODJ with l1 regularization. From the damage identification results, it can be seen that the proposed BBPSODJ algorithm, which is efficient and robust, has great potential in the field of SHM.