Three-dimensional carbon nanotube field-effect transistors (3D CNTFETs) possess predictable characteristics that rival those of planar CNTFETs and Si-based MOSFETs. However, due to the lack of a reliable assembly technology, they are rarely reported on, despite the amount of attention they receive. To address this problem, we propose the novel concept of a 3D CNTFET and develop its assembly strategy based on nanomanipulation and the electron-beam-induced deposition (EBID) technique inside a scanning electron microscope (SEM). In particular, the electrodes in our transistor design are three metallic cuboids of the same size, and their front, top and back surfaces are all wrapped up in CNTs. The assembly strategy is employed to build the structure through a repeated basic process of pick-up, placement, fixing and cutting of CNTs. The pick-up and placement is performed through one nanomanipulator with four degrees of freedom. Fixing is carried out through the EBID technique so as to improve the mechanical and electrical characteristics of the CNT/electrodes connection. CNT cutting is undertaken using the typical method of electrical breakdown. Experimental results showed that two CNTs were successfully assembled on the front sides of the cubic electrodes. This validates our assembly method for the 3D CNTFET. Also, when contact resistance was measured, tens of kilohms of resistance was observed at the CNT-EBID deposition-FET electrodes junction.. This manifests the electrical reliability of our assembly strategy.