Objective A single hidden layer feed-forward neural network training method based on extreme learning machine ELM was proposed for pantograph delay differential equations and the method was extended to deal with the system of pantograph equations with two delays. Methods Firstly a feed-forward neural network with a single hidden layer was constructed and the input weights and hidden layer bias were randomly generated. Then by calculating the coefficient matrix to satisfy the pantograph delay differential equation and its initial value conditions the equation was transformed into a least squares problem and the output weight was obtained by using the Moor-Penrose generalized inverse solution. Finally the numerical solution of the pantograph delay differential equation with high precision could be obtained by inputting the output weights into the constructed neural network. Results By comparing the results of numerical experiments with those of existing methods the effectiveness of the proposed method in dealing with pantograph delay differential equations and the system of pantograph equations with two delays was verified. With the increase in the number of selected training points and hidden layer nodes the accuracy and convergence rate of the numerical solutions were also increased. Conclusion The ELM algorithm is effective in dealing with pantograph delay differential equations and the system of pantograph equations with two delays.