We have developed fully non-blocking optical matrix switches using a thermo-optic polymer 1 × 2 total-internal-reflection (TIR) switch as a unit switching element. The TIR switch consists of crossed multimode polymer waveguides and an offset heater electrode at the switching node. The fabricated 4 × 4 and 8 × 8 optical matrix switch chips show excellent switching performances. The insertion losses are less than 2.5 and 4.5 dB for the 4 × 4 and 8 × 8 matrix switches, respectively, and their switching isolations during a turned-off state are higher than 38 dB. The switching time is about 3 ms, and the power consumption for each switching element is below 30 mW. Compact integration of the 4 × 4 and 8 × 8 switch chips is achieved at sizes of 25 mm × 4.25 mm, and 42.4 mm × 5 mm, respectively, through an optimization of the waveguide and heater geometries.