A neural network-based design method for thermoacoustic Stirling engines (TASE) is presented in this work. The main goal of the article is to predict the design parameters (Length of resonator (stub) (LR), Length of inertance tube (Lin), Mean pressure (Pm)) of the thermoacoustic Stirling engine in such a way that the dynamic instability is guaranteed. In this regard, the governing equations of the engine are presented first. Next, with the help of the data extracted from the simulation of the governing equations of the engine, a neural network with the structure of 9–35-3 is trained. The effectiveness of the artificial neural network (ANN) structure is explored via regression and MSE (mean square error) analyses. Next, in order to evaluate and validate the neural network, the experimental data of the constructed thermoacoustic Stirling engine (SUTech-SR-4) is considered. It is important to note that the SUTech-SR-4 is introduced for the first time in this work. Investigations have shown that the neural network could estimate the engine design parameters well and with an acceptable approximation in such a way that the dynamic instability of the engine is also established. Besides, the value of the estimated design parameters for the engine made by the neural network was close to the experimental values. Following, the developed engine is introduced and its performance is discussed. The developed engine has been able to produce a power equivalent to 0.346 W at a pressure of 1 bar (with air working fluid) and a working frequency of 15.9 Hz. It should be noted that the method presented in this article can be used for other types of thermoacoustic Stirling engines. Moreover, the selection of design parameters for the presented method will depend on the physics of the engine and the available facilities.