  We study classical spinning closed string configuration on logarithmically
deformed AdS_5 x T^{1,1} background with non-trivial Neveu-Schwarz B-field in
which IIB string theory is dual to a non-conformal N=1 SU(N+M) x SU(N) gauge
theory. The integrability on original AdS_5 x T^{1,1} background are
significantly reduced by B-field. We find several spinning string solutions
with two different ansatzs. Solutions for point-like strings and few circular
strings are explicitly obtained. Folded spinning string solutions along radial
direction are shown to be allowed in this background. These solutions exhibit
novel properties and bring some challenges to understand them from dual quantum
field theory.
