Wormhole solutions obtained by Morris and Thorne (MT) in general relativity (GR) is investigated in a modified theory of gravity. In the gravitational action, we consider f(R, T) which is a function of the Ricci scalar (R) and the trace of the energy-momentum tensor (T). In the framework of a modified gravity described by f(R,T)=R+αR2+λTβ\documentclass[12pt]{minimal}
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\begin{document}$$f(R,T)=R+\alpha R^{2}+\lambda T^{\beta }$$\end{document}, where α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}, β\documentclass[12pt]{minimal}
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\begin{document}$$\beta $$\end{document} and λ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda $$\end{document} are coupling constants, MT wormhole (WH) solutions with normal matter are obtained for a relevant shape function. We have considered two different values of β\documentclass[12pt]{minimal}
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\begin{document}$$\beta $$\end{document} leading to two forms of f(R, T)-gravity. The energy conditions are probed at the throat and away from the throat of the WH. It is found that the coupling parameters, α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document} and λ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda $$\end{document} in the gravitational action play an important role in deciding the matter composition in the wormholes. It is found that for a given λ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda $$\end{document}, WH exists in the presence of exotic matter at the throat when α<0\documentclass[12pt]{minimal}
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\begin{document}$$\alpha <0$$\end{document}. It is demonstrated here that WH exists even without exotic matter for α>0\documentclass[12pt]{minimal}
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\begin{document}$$\alpha >0$$\end{document} in the modified gravity. Two different shape functions are considered to obtain WH solutions that are permitted with or without exotic matter. It is noted that in a modified f(R, T) gravity MT WH is permitted with normal matter which is not possible in GR. It is demonstrated that a class of WH solutions exist with anisotropic fluid for λ≠-8π\documentclass[12pt]{minimal}
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\begin{document}$$\lambda \ne -8\pi $$\end{document}. However, for flat asymptotic regions with anisotropic fluids WH solutions cannot be realized when λ=-8π\documentclass[12pt]{minimal}
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\begin{document}$$\lambda =-8\pi $$\end{document}. All the energy conditions are found consistent with the hybrid shape function indicating existence of WH even with normal matter for λ→0\documentclass[12pt]{minimal}
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\begin{document}$$\lambda \rightarrow 0$$\end{document}.
