Membrane tension is a core parameter in the construction and use stages of membrane structures, However, the long-standing lack of effective engineering application methods of membrane tension measurement has been a bottleneck in this field. This paper develops an active adsorption central pushing tension equilibrated membrane tensiometer based on the principle of static load displacement method. The membrane tensiometer uses a suction cup to adsorb the membrane surface, creating a normal constraint boundary circular membrane surface, applies thrust to the center of the membrane surface, measures the thrust force and membrane surface deformation, and calculates the bidirectional membrane tension. It simultaneously achieves automated control of the tensiometer measurement, data acquisition, and transmission, as well as remote control and data transmission. This paper presents the calibration formula for tension measurement using the membrane tensiometer and conducts calibration tests on P, G, and E type membranes, obtaining corresponding fitting parameters. Tension measurement verification was performed on P and G type membranes, with the membrane tensiometer showing a maximum error of less than 10% in tension measurements across a reasonable biaxial tension range in membrane structure of 1.5 to 6.0 kN/m and a stress ratio range of 1:1 to 1:4, demonstrating high measurement accuracy suitable for practical engineering applications.