We construct a manifestly N=3 supersymmetric low-energy effective action of N=3 super Yang-Mills theory. The effective action is written in the N=3 harmonic superspace and respects the full N=3 superconformal symmetry. On mass shell this action is re
sponsible for the four-derivative terms in the N=4 SYM effective action, such as F^4/X^4 and its supersymmetric completions, while off shell it involves also higher-derivative terms. For constant Maxwell and scalar fields its bosonic part coincides, up to the F^6/X^8 order, with the bosonic part of the D3 brane action in the AdS_5 x S^5 background. We also argue that in the sector of scalar fields it involves the correctly normalized Wess-Zumino term with the implicit SU(3) symmetry.
