By means of the field-theoretic renormalization group, we study the damping of the viscosity coefficient near the superfluid phase transition. We use the fact that in the infrared region, the complex model used to describe the phase transition belongs to the same universality class as the well-known stochastic model A. This allows us to determine the critical behavior of viscosity using composite operators for model A. Our analysis is based on the $\varepsilon$-expansion near the upper critical dimension $d_{\mathrm c} =4$ of model A. The critical exponent of viscosity is then calculated from the critical dimensions of composite operators of massless two-component model A. In particular, we present results for critical dimensions of a selected class of composite operators with the canonical dimension $8$ to the leading order.