Groove is a key structure of high-performance integral cutting tools. It has to be manufactured by 5-axis grinding machine due to its complex spatial geometry and hard materials. The crucial manufacturing parameters (CMP) are grinding wheel positions and geometries. However, it is a challenging problem to solve the CMP for the designed groove. The traditional trial-and-error or analytical methods have defects such as time-consuming, limited-applying and low accuracy. In this study, the problem is translated into a multiple output regression model of groove manufacture (MORGM) based on the big data technology and AI algorithms. The input are 34 groove geometry features and the output are 5 CMP. Firstly, two groove machining big data sets with different range are established, each of which is includes 46656 records. They are used as data resource for MORGM. Secondly, 7 AI algorithms, including linear regression, k nearest-neighbor regression, decision trees, random forest regression, support vector regression and ANN algorithms are discussed to build the model. Then, 28 experiments are carried out to test the big data set and algorithms. Finally, the best MORGM is built by ANN algorithm and the big data set with a larger range. The results show that CMP can be calculated accurately and conveniently by the built MORGM.