The invention discloses a tension-leg offshore floating wind turbine foundation capable of floating and being installed by self and an installation method thereof. The tension-leg offshore floating wind turbine foundation comprises three rectangular floating boxes on a same horizontal plane and of which any two are at an included angle of 120 degrees, a center floating box connecting the three rectangular floating boxes, a center pillar connected with the upper end of the center floating box and used for supporting a wind turbine tower, three peripheral pillars which are in a one-to-one connection with the three rectangular floating boxes and separated from each other, three cantilever beams respectively and correspondingly arranged at the top of the three peripheral pillars and extending outwardly, a heave plate connected to the bottom of the three rectangular floating boxes and the center pillar, transverse braces and diagonal braces for connecting the center pillar and the peripheral pillars, a subsea base part and tension legs for connecting the cantilever beams and the subsea base part. The tension-leg offshore floating wind turbine foundation capable of floating and being installed by self according to an embodiment of the invention has the advantages of low cost for later maintenance, convenient installation and low installation cost.