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We define the Euclidean hull of a linear code $C$ as the intersection of $C$and its Euclidean dual $C^\perp$. The hull with low dimensions gets muchinterest due to its crucial role in determining the complexity of algorithmsfor computing the automorphism group of a linear code and checking permutationequivalence of two linear codes. It has been recently proved that any $q$-ary$[n,k]$ linear code with $q>3$ gives rise to a linear code with the sameparameters and having zero dimensional Euclidean hull, which is known as alinear complementary dual code. This paper aims to explore explicitconstructions of families of MDS linear codes with one dimensional Euclideanhull. We obtain several classes of such codes.

MDS linear codes with one dimensional hull