This paper presents a novel bacterial swarming algorithm (BSA) for global optimization. This algorithm is inspired by swarming behaviors of bacteria, in particular, focusing on the study of tumble and run actions which are the major part of the chemotactic process. Adaptive tumble and run operators are developed to improve the global and local search capability of the BSA, based on the existing bacterial foraging algorithm (BFA). Simplified quorum-sensing mechanism is also incorporated to enhance the performance of this algorithm. BSA has been evaluated, in comparison with existing evolutionary algorithms (EAs), such as fast evolutionary programming (FEP) and particle swarm optimizer (PSO), on a number of mathematical benchmark functions. The simulation studies have been undertaken and the results show that the BSA can provide superior performance than FEP and PSO in optimizing these benchmark functions, particularly, in terms of its convergence rates and robustness.