Neural networks are becoming ubiquitous in various areas of physics as a successful machine learning (ML) technique for addressing different tasks. Based on ML technique, we propose and experimentally demonstrate an efficient method for state reconstruction of the widely used Sagnac polarization-entangled photon source. By properly modeling the target states, a multi-output fully connected neural network is well trained using only six of the sixteen measurement bases in standard tomography technique, and hence our method reduces the resource consumption without loss of accuracy. We demonstrate the ability of the neural network to predict state parameters with a high precision by using both simulated and experimental data. Explicitly, the mean absolute error for all the parameters is below 0.05 for the simulated data and a mean fidelity of 0.99 is achieved for experimentally generated states. Our method could be generalized to estimate other kinds of states, as well as other quantum information tasks.