Full tensor gravity gradiometers based on accelerometer pair combination are widely employed in earth resource explorations using gravity gradient measurements. However, the extremely high requirements of accelerometer dynamic range and the scale factor consistency of accelerometer pairs are the two main limitations to further improve their performances. In order to overcome these two extreme challenges, the torque type gravity gradiometer based on the Etövös torsion balance pendulum is re-considered. In this paper, an improved torque type full tensor gravity gradiometer with a flexure-strip suspension is proposed, which balances the mechanical sensitivity and the response time. The proposed gradiometer can be used to measure the full tensor gravity gradient by observing angle variations at three azimuths. The principle and feasibility of the torque type full tensor gravity gradiometer based on a flexure-strip suspension are introduced, and the main noise sources including mechanical thermal noise, position sensing noise, and readout noise are analyzed. A prototype gravity gradiometer with a designed resolution of 2 E/Hz1/2 at 0.1 Hz is constructed (1 E = 10-9/s2), and the experimental results indicate that its resolution comes to 3 E/Hz1/2 at 0.1 Hz, which is mainly limited by the seismic noise. This type of gravity gradiometer can be further improved due to its high potential resolution and independence of matching combination requirement, which allows it to be applied in next generation gravity resource exploration.