In this paper, A new method is applied to approach function -The Broad Learning System (BLS). Due to the complexity of the system in actual engineering, when the traditional algorithm handles the approximation problem, it faces problems such as complicated calculations and severe time consumption. To solve the above problems, the BLS uses the way of network horizontal expansion, horizontal extension and vertical immobility. Input data is mapped to feature nodes as feature vectors of the network, and then connected enhancement nodes by random weights, the enhancement node and the function node are spliced together as an input layer, and then directly connected to the output of the system. Finally, compared with traditional algorithms: back propagation neural network (BPNN), Radial Basis Function neural network (RBFNN), the results of experiments show that the function approximation method based on the BLS in this paper can make the system use less time under the premise of ensuring the approximation accuracy. This result provides the possibility of real-time and high-precision approximation for other intelligent algorithms.