The invention relates to a unidirectional plunger type oil cylinder of a hydraulic press, which comprises a cylinder body, a plunger rod, a guide structure and a sealing element, wherein the guide structure and the sealing element are arranged between the cylinder body and the plunger rod, the unidirectional plunger type oil cylinder is characterized in that a cylindrical cavity is processed on the lower end of the plunger rod, a first spherical surface pad and a spherical surface column in spherical surface fit are arranged in the cylindrical cavity from the top down, the first spherical surface pad is fixedly installed on the plunger rod, the spherical surface column stretches out from the lower end of the plunger rod, a supporting sleeve fixedly installed on the lower end of the plunger rod is sleeved at the outside of the spherical surface column, a lug boss is processed at the outside of the lower end of the supporting sleeve, a bracket structure fixedly connected with a middle cross beam is erected on the lug boss, and an elastic pad is arranged between the bracket structure and the lug boss; and a second spherical surface pad fixedly connected with the middle cross beam is installed in the lower end of the supporting sleeve, the second spherical surface pad and the lower end of the spherical surface column are in spherical surface fit with each other. Under the partial load processing condition of the oil cylinder, the second spherical surface pad rotates along the matching surface of the spherical surface column and the spherical surface column rotates along the matching surface of the first spherical surface pad to prevent the plunger rod from deflecting along the axial line and enable the plunger rod to move linearly up and down, so as to reduce the strain damage on the cylinder body and the plunger rod.