This paper focuses on a neural network-based structure for predicting significant unmeasurable parameters of a free-piston Stirling oscillator (FPSO). First, the nonlinear dynamic and thermodynamic equations governing a prototype FPSO are extracted. Then, a systematic approach for developing artificial neural network (ANN) is presented to predict the values of five unknown parameters considering nine measurable inputs. The critical unknown parameters include the damping coefficients of power and displacer pistons, the damping coefficient between displacer rod and power piston, and the gas temperatures within the compression and expansion spaces. Subsequently, the proposed ANN is trained and then, the regression analysis as well as the performance evaluation is carried out to validate the obtained ANN model. Furthermore, in order to verify the performance of the proposed ANN model, although limited empirical information is available, the experimental results collected from two prototype FPSOs namely SUTech-SR-1 and B10-B are compared to the ANN outcomes. Moreover, the practical P-V diagrams of the mentioned oscillators, under various realistic operating conditions, are compared to the predictions obtained from the ANN for further verification of the proposed model. Lastly, it is found that the prediction error is less than 4% which affirms the capability of the proposed technique to estimate the unmeasurable parameters of FPSOs.