A novel output-feedback super-twisting algorithm design is proposed for uncertain multivariable plants. In order to allow global finite-time exact tracking in the presence of a rather general class of matched nonlinear disturbances which may depend on measured and/or unmeasured states, the algorithm is designed with variable gains. This represents a significant extension of a recently proposed nondecoupled multivariable super-twisting algorithm, based on state-feedback with fixed gains, to the case of output-feedback with variable gains.