The self-organizing map (SOM), as a kind of unsupervised neural network, has been applied for both static data management and dynamic data analysis. To further exploit Its ability in search, in this paper, we employ the SOM as a searching mechanism for dynamic system. A learning scheme, consisting mainly of the SOM and the target dynamic system, Is then proposed. The performance of this SOM-based learning scheme is especially compared with that of the genetic algorithm (GA) due to their resemblance in learning and searching. And, a new SOM weight updating rule Is proposed to enhance learning efficiency, which may dynamically adjust the neighborhood function for the SOM in learning system parameters. For demonstration, the proposed learning scheme is applied for trajectory prediction, and Its effectiveness evaluated via the simulations based on using the SOM, GA, and also Kalman filtering.