Solid rocket motors (SRMs) have been a critical component of space exploration, military operations, and numerous other applications for decades. The ability to accurately predict the ignition transient behavior of solid rocket motors is crucial for ensuring safe and reliable operations. In this study, artificial neural networks (ANNs) are employed to predict the ignition transient process of a model solid rocket motor. The training and validation data for the ANNs are obtained through simulations of a validated quasi-one-dimensional model. Results show that with the inputs of axial coordinate and igniting time, the ANNs can predict density, axial velocity, temperature, and pressure in internal ballistic within 0.039 relative error and a correlation coefficient above 0.994 compared to the quasi-one-dimensional simulations in millisecond level. With the increase of hidden layers and neural numbers in the ANNs, prediction accuracy increases. When the hidden layers exceed four, prediction accuracy cannot improve significantly. When test data is out of the temporal range of the training and validation data, prediction accuracy decreases evidently. The trained ANN model can be used to predict solid rocket motors with increased internal ballistic spatial resolution within 0.007 relative error and to predict solid rocket motors with increased temporal resolution within 0.107 relative error.