This paper deals with the existence of positive ω-periodic solutions for third-order ordinary differential equation with delay \t\t\tu‴(t)+Mu(t)=f(t,u(t),u(t−τ)),t∈R,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$u'''(t)+Mu(t)=f\\bigl(t,u(t),u(t-\\tau) \\bigr),\\quad t\\in {\\mathbb{R}}, $$\\end{document} where omega>0 and M>0 are constants, f: {mathbb{R}}^{3}rightarrow {mathbb{R}} is continuous, f(t,x,y) is ω-periodic in t, and tau>0 is a constant denoting the time delay. We show the existence of positive ω-periodic solutions when 0< M<(frac{2pi}{sqrt {3}omega})^{3} and f satisfies some order conditions. The discussion is based on the theory of fixed point index.