String-net condensate is a new class of materials which exhibits quantum topological order. Here we study the measurement-based quantum computation on the simplest example of string-net condensate, namely the Z2 gauge string-net condensate on the two-dimensional hexagonal lattice, by using the framework of quantum computational tensor network. We show that universal measurement-based quantum computation is possible by coupling two correlation space wires with a physical two-body interaction. We also show that universal measurement-based quantum computation is possible solely with single-qubit measurements if the sign of the coefficient of each closed-loop configuration in the state is tuned. These results suggest that even the simplest example of string-net condensate is equipped with the correlation space that has the capacity for the application to quantum information processing.