The invention discloses an auxiliary device capable of adjusting jacking pipe stress and a construction method, and belongs to a jacking pipe jacking construction method. The auxiliary device comprises a jacking pipe pit, a jacking pipe, a jack, a limiting rod, a first connecting plate, a second connecting plate and a fitting piece, wherein a groove is formed inside the limiting rod, a shell bodyof the jack is installed inside the groove, one side surface of the first connecting plate is fixedly connected with the wall of the jacking pipe pit, and the other side surface of the first connecting plate is fixedly connected with the limiting rod; the second connecting plate is located at the end, away from the first connecting plate, of the limiting rod, the second connecting plate is fixedlyconnected with a plunger of the jack, and the side, back to the plunger, of the jack is fixedly connected with the first connecting plate; and the fitting piece comprises an arc-shaped crawler frameand push cylinders, the arc-shaped crawler frame is located on the side, back to the jack, of the second connecting plate, and the push cylinders are evenly distributed inside the arc-shaped crawler frame. According to the auxiliary device, the problem of later-period maintenance such as cracks caused by different jacking force distribution of the jacking pipe is solved, so that the probability ofcracking of the jacking pipe is reduced, and the problems such as the later-period maintenance cost are reduced.