Civil engineering structures are subject to both static and dynamic loadings. This applies especially to buildings in seismic areas as well as bridges, viaducts, and road and railway structures loaded with road or rail traffic. One of the solutions used to repair and strengthen such structures in the event of emergency damage are fibre-reinforced polyurethanes (FRPUs). The article proposes a laboratory method for determining the dynamic complex modulus of FRPU composite tape. The theoretical basis for determining the complex modulus for the tested material is presented. Laboratory tests were carried out using the tensile method for four cyclic loading frequencies and a cyclic load ratio equal to 0.5. Under the assumed test conditions, the material showed a viscoelastic performance with a dominant elastic part (storage modulus). For a frequency of 0.1 Hz, the viscous part (loss modulus) was about 8% of the storage modulus value, while for a frequency of 10 Hz, this value was about 5%. For a loading frequency of 0.1 Hz, the elastic part of the complex modulus was about 1160 MPa, while for a frequency of 10 Hz, it was about 1790 MPa. With the increase in loading frequency, the absolute value of the complex modulus increased.