Current neural network methods solving Differential-Algebraic Equations （DAEs） basically adopt data-driven strategies， and require a large number of datasets. So that， there are problems such as sensitive structure and parameter selection of neural networks， low accuracy of solution， and poor stability. In response to these issues， a Physics-Informed Neural Network based on Lobatto method and Legendre polynomials （LL-PINN） was proposed. Firstly， based on the discrete Physics-Informed Neural Network （PINN） computing framework， combined with the advantages of high accuracy and high stability of Lobatto IIIA method solving DAEs， the physical information of DAEs was embedded in the Lobatto IIIA time iteration format， and PINN was used to solve the approximate numerical value of this time iteration. Secondly， a neural network structure with single hidden layer was utilized， by using the approximation capability of Legendre polynomials， these polynomials were applied as activation functions to simplify the process of adjusting the network model. Finally， a time domain decomposition scheme was employed to construct the network model， which a differential neural network and an algebraic neural network were used for each equally divided sub-time domain one by one， enabling high-precision continuous-time prediction of DAEs. Results of numerical examples demonstrate that the LL-PINN based on Legendre polynomials and the 4th-order Lobatto method achieves high-precision solutions for DAEs. Compared to the Theory of Functional Connections （TFC） trial solution method and PINN model， LL-PINN significantly reduces the absolute error between the predicted and exact solutions of differential variables and algebraic variables， and improves accuracy by one or two orders of magnitude. Therefore， the proposed solution model exhibits good computational accuracy for solving DAE problems， providing a feasible solution for challenging partial DAEs.