A finite volume method (FVM) base on the SIMPLE algorithm as the pressure correction strategy and the traditional staggered mesh is used to investigate steady, fully developed flow of Oldroyd-3-constant fluids through a duct with square cross-section. Both effects of the two viscoelastic material parameters, We and ${mu}$, on pattern and strength of the secondary flow are investigated. An amusing sixteen vortices pattern of the secondary flow, which has never been reported, is shown in the present work. The reason for the changes of the pattern and strength of the secondary flow is discussed carefully. We found that it is variation of second normal stress difference that causes the changes of the pattern and strength of the secondary flow.