This paper presents a fuzzy neural network for learning the knowledge of a fuzzy logic rule-based system. The network contains five layers: an Input Layer, Membership-function Layer, AND Layer, OR Layer, and Defuzzification Layer. We propose a backpropagation-like learning algorithm to train this neural network to acquire the fuzzy rules and to fine-tune the knowledge on the parameters of AND and OR nodes. Compared with methods other than the gradient descent search, the proposed learning process acquires more precise knowledge. In addition, the functions of the AND and OR nodes in the network are formulated with the minimum or maximum operations, respectively. Therefore, the adjustments of the learnable weights (parameters) can be focused on the dominant terms related to the (minimum/maximum) operations. The convergence time for the proposed learning algorithm is much faster than that for conventional backpropagation algorithms. In summary, the learnable weights (parameters) of the network are adjusted very quickly to obtain precise knowledge. Simulation results show that in learning the truck backer-upper problem, our network completes the training procedure in only several dozen epochs with an error rate of less than 1%.