We consider a specific deformed Bose gas model constructed by the so-called Tamm-Dancoff oscillators whose spectrum has exponential cutoff factors at high energies. We investigate, in the thermodynamical limit, the effects of Tamm-Dancoff type deformation on the low-temperature behavior of the system through a generalized Bose-Einstein distribution. In particular, we show that the Bose-Einstein condensation would occur in such a model just for values of the deformation parameter q in the range q > 1. Besides, from the Fock space representations of the model algebra, it is interestingly showed that the present boson model exhibits fermion-like behavior in the limit q -> infinity. (C) 2013 Elsevier B.V. All rights reserved.