Nonlinear　normal　modes　and　a　numerical　iterative　approach　are　applied　to　study　the　parametric　vibrations　of　pipes　conveying　pulsating　fluid　as　an　example　of　gyroscopic　continua.　The　nonlinear　non-autonomous　governing　equations　are　transformed　into　a　set　of　pseudo-autonomous　ones　by　employing　the　harmonic　balance　method.　The　nonlinear　normal　modes　are　constructed　by　the　invariant　manifold　method　on　the　state　space　and　a　numerical　iterative　approach　is　adopted　to　obtain　numerical　solutions,　in　which　two　types　of　initial　conditions　for　the　modal　coefficients　are　employed.　The　results　show　that　both　initial　conditions　can　lead　to　fast　convergence.　The　frequency-amplitude　responses　with　some　modal　motions　in　phase　space　are　obtained　by　the　present　iterative　method.　Quadrature　phase　difference　and　traveling　waves　are　found　in　the　time-domain　complex　modal　analysis.