An　illumination　beam　with　a　subwavelength　waist　and　extended　focal　depth　is　ideal　for　terahertz　computed　tomography.　In　this　paper,　a　binary　terahertz　super-oscillatory　lens　is　proposed　with　a　full　width　at　half-maximum　of　0.97　A,　a　focal　length　of　48　A,　a　focal　depth　of　25　A,　and　a　numerical　aperture　of　0.24.　It　was　designed　using　the　simulated　annealing　algorithm,　fabricated　by　three-dimensional　printing,　and　applied　in　continuous-wave　terahertz　computed　tomography　operating　at　278.6　GHz.　When　combined　with　the　total　variation　minimisation　algorithm,　this　setup　was　able　to　recognise　a　hollow　cylinder　with　wall　thickness　1.1　A　and　a　bar　of　diameter　0.93　A　inside　a　chamber,　with　mean　errors　of　less　than　5%.　Our　approach　provides　an　effective　way　to　enhance　the　resolution　and　reconstruction　fidelity　of　terahertz　computed　tomography　and　to　promote　it　as　an　effective　tool　for　non-destructive　testing　and　three-dimensional　measurement.