In this paper, we provide a biasing expansion swarm approach (BESA) for using multiple simple mobile agents, with limited sensing and communication capabilities, to collaboratively search and locate an indeterminate number of emission sources in an unknown large-scale area. The key concept in this approach is swarm behavior. By applying the three properties of the swarm behavior: separation, cohesion and alignment, our approach can ensure the agent group attains dynamically stable ad-hoc connectivity and fast target convergence. Using a grid map to represent the unknown environment, an ad-hoc network for wireless communication and our biasing expansion algorithm for path planning, each agent simultaneously considers all concentration values collected by other swarm members and determines the positive gradient direction of the whole coverage area of the swarm. This will make the swarm immune to the random sensor errors, local aerosol accumulations and other local interference effects during their search. We present a simulated environment that has multiple emission sources and complex aerosol accumulation and distribution. Based on the simulation, our approach can achieve better performance than the gradient descent approach, which currently appears to be the most popular algorithm for emission source localization.