In the present paper, we give the global L^{q} estimates for maximal operators generated by multiparameter oscillatory integral S_{t,varPhi}, which is defined by \t\t\tSt,Φf(x)=(2π)−n∫Rneix⋅ξei(t1ϕ1(|ξ1|)+t2ϕ2(|ξ2|)+⋯+tnϕn(|ξn|))fˆ(ξ)dξ,x∈Rn,\\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}$$S_{t,\\varPhi}f(x)=(2\\pi)^{-n} \\int_{\\mathbb{R}^{n}} e^{ix\\cdot\\xi}e^{i(t_{1} \\phi_{1}(|\\xi_{1}|)+t_{2}\\phi_{2}(|\\xi_{2}|)+ \\cdots+t_{n}\\phi_{n}(|\\xi_{n}|))}\\hat{f}(\\xi)\\,d\\xi,\\quad x\\in\\mathbb{R}^{n}, $$\\end{document} where ngeq2 and f is a Schwartz function in mathcal{S}(mathbb {R}^{n}), t=(t_{1},t_{2},ldots,t_{n}), varPhi=(phi_{1},phi_{2},ldots,phi_{n}), phi_{i}(i=1,2,3,ldots, n) is a function on mathbb {R}^{+}rightarrowmathbb{R}, which has a suitable growth condition. These estimates are apparently good extensions to the results of Sjölin and Soria (J. Math. Anal. Appl 411:129–143, 2014) for the multiparameter fractional Schrödinger equation.