The precise determination of the center of a laser beam holds significant importance across various domains, particularly within laser manufacturing and machining systems, owing to its exceptional precision and efficient operational capabilities. Nevertheless, the identification of the center of intersecting beams presents a complex challenge. In response, a novel approach integrating convolutional neural networks and advanced image processing techniques has been introduced to accurately ascertain the center position of intersecting beams. Our method commences with the utilization of a convolutional neural network to extract two significant features: the ratio between the minor and major axes and the orientation angle of two beams. Simultaneously, perform the affine transformation algorithm to transform the beam with an elliptical profile into a circular beam. Subsequently, the center position of each beam is calculated through the Euclidean distance transform method. The result demonstrates that our method accurately identifies the centers of overlapping points in real time.