In this paper we consider global Morrey spaces with variable exponents p(.), θ(.), where  is an unbounded set. The questions of boundedness of the singular integral operator and its commutator in these spaces are investigated. We give the conditions for the variable exponent and for the functions ( (.),  (.)) under which the singular integral operator  will be bounded from  to . The same conditions  for the boundedness of the commutator of the singular integral operator in these spaces are obtained.. In the case when the exponents   are constant numbers, the questions of boundedness of the singular integral operator and its commutator in global spaces were previously studied by other authors. There are also well-known results on the boundedness of a singular integral operator in the  global Morrey-type spaces with variable exponents when the set   is bounded.