A novel Jacobi neural network method is proposed for solving linear differential-algebraic equations (DAEs) in the paper. First, Jacobi neural network is applied to derive the approximate solutions form of DAEs, and the loss function is constructed for DAEs based on single hidden layer Jacobi neural network structure. Then, we get the optimal output weights of Jacobi neural network by applying extreme learning machine algorithm. In particular, Legendre neural network method and Chebyshev neural network method which have been widely used by scholars are special cases of Jacobi neural network method, and the numerical results of the proposed method are better than these of Legendre neural network method and Chebyshev neural network method. Furthermore, Jacobi neural network method has higher accuracy compared with the approximate analytical methods, the numerical comparison results further show the feasibility and effectiveness of the proposed method for solving the DAEs.