The intellectual property (IP) mapping problem is an NP-hard problem in network-on-chip (NoC) designs and is often solved by the genetic Algorithm. In the genetic algorithm (GA), new populations are generated by crossover and mutation operators. However, these operators consider neither the prior knowledge of the IP mapping problem nor the historical experience of the population evolution, easily causing the GA to converge prematurely to the local optima. To solve this problem, a learnable model-based GA (LMGA) is proposed, which introduces a learnable model and a hybridization scheme of the model and GA. 1) the learnable model is implemented by a novel neural network-based probability model for the IP mapping problem, i.e., the message passing attention network (MAN). Moreover, the learnable model is pretrained then updated by learning the features of high-fitness individuals among the population to predict a better probability distribution of the optimal solution in a specific IP mapping problem. 2) The scheme updates the population of certain generations of the GA by sampling the learnable model. Hence, the population evolution is guided by the learnable model to avoid premature convergence. Simulation results show that the MAN achieves a faster training speed and models the large-scale IP mapping problem better than the message passing neural network-pointer network (MPN) in the previous work. The LMGA saves an average of 5.68% and 5.23% in the communication energy and average network delay, respectively, than the state-of-the-art algorithm, i.e., the message passing neural network-pointer network-based genetic algorithm (MPN-GA).