The “Composite Light Source” project of the National Synchrotron Radiation Laboratory, Terahertz Near-Field High-Flux Material Property Testing System, consists of an approximately 3-meter electron linear accelerator. To characterize the performance of the accelerator and monitor the status of the beam, it is necessary to measure the beam size. Specifically designed for the terahertz linear accelerator, a beam size measurement system based on the EPICS distributed system has been developed. A beam spot detector is taken for the conversion of the beam spot into an optical spot and a remote mirror is taken to image the optical spot onto a CCD camera for image acquisition. Subsequently, the camera-captured image data is integrated into the EPICS database using ADAravis. Due to the dark current and radiation environment, salt-and-pepper noise is present in the acquired images. Therefore, a Convolutional Neural Network (CNN) is employed to suppress the salt-and-pepper noise in the images. Finally, Gaussian fitting is applied to calculate the beam cross-sectional dimensions from the images. The experimental results indicate that the CNN can effectively eliminate salt-and-pepper noise, and the resolution of this system is 15.8 μm, which satisfies the design requirement.