In this paper, the log-conformation representation method (LCR) is applied in an orthogonal curvilinear coordinate system to study the Giesekus fluid flow in a curved duct. Derivations for evolution equations of LCR in this curvilinear coordinate system are presented. Secondary flow patterns and oscillation solutions are computed by using the collocation spectral method. The influence of a wide range of Dean number, Weissenberg number, and dimensionless mobility parameter α on fluid behaviors is studied. A six-cell secondary flow pattern is found under very low Dean number and relatively high Weissenberg number and α. Moreover, both Weissenberg number and α are able to facilitate the development of the secondary flow. In addition, simulations under critical Reynolds number for oscillation imply that Giesekus fluid flow with [Formula: see text] is not able to retain a four-cell secondary flow pattern in a steady state, which is different from Newtonian fluids.