Abstract Jet pumps are widely used in thermoacoustic Stirling heat engines and pulse tube cryocoolers to restrain acoustic streaming and improve the system performance. In this paper, a regression model is presented to predict the acoustic streaming in a thermoacoustic Stirling heat engine (TASHE) with different structure parameters of the jet pump. These parameters include position, length, inner diameter and tapered angle. Response surface methodology (RSM) is used to study the relationship between structure parameters of jet pump and acoustic streaming. A regression model is developed to predict the acoustic streaming. The analysis of variance (ANOVA) is conducted to describe the rationality of regression model and examine the statistical significance of factors. In addition, the relationship between acoustic streaming and structure parameters of jet pump is presented using 2D contour and 3D surface plot. It reveals that small position, length, tapered angle and large inner diameter can help suppress acoustic streaming. Eventually, four random confirmation tests are performed to verify that the regression model can predict acoustic streaming reasonably. This work provides theoretical guidance for controlling acoustic streaming using jet pump.