The invention provides a mobile hydraulic pressure test machine oil well pipe stabilizing device comprising a base beam, a bearing beam, a travelling trolley, and a control system. The base beam is fixedly connected with a frame of the hydraulic pressure test machine. A push-pull cylinder is arranged on the base beam. A lug is provided on the bearing beam. The piston rod of the push-pull cylinder is connected with the lug. One side of the bearing beam is provided with a coupling stop head. A semi-cylindrical groove matching the oil well pipe is arranged on the coupling stop head. The bottom of the bearing beam is fixedly connected with the travelling trolley. A base beam recess and a bearing beam recess are respectively provided on the middles of the base beam and the beating beam. With the device provided by the invention, a problem of oil well pipe instability caused by large axial forces is solved, and an oil well pipe axial shift problem is solved. The device has the advantages of simple structure and reasonable arrangement. With the device, coupling stop head replacement can be realized simply and rapidly. The device is safe and reliable, and is suitable for hydraulic pressure tests of oil well pipes with various diameters.