Polymers adopt extended coil and compact globule states according to the balance between entropy and interaction energies. The transition of a polymer between an extended coil state and compact globule state can be induced by changing thermodynamic force such as temperature to alter the energy/entropy balance. Previously, this transition was theoretically studied by taking into account the excluded-volume interaction between monomers of a polymer chain using the partition function. For binary mixtures of a long polymer and short polymers, the coil-globule transition can be induced by changing the concentration of the shorter polymers. Here, we investigate the transition caused by short polymers by generalizing the partition function of the long polymer to include the excluded-volume effect of short polymers. The coil-globule transition is studied as a function of the concentration of mixed polymers by systematically varying Flory's χ-parameters. We show that the transition is caused by the interplay between the excluded-volume interaction and the dispersion state of short polymers in the solvent. We also reveal that the same results can be obtained by combining the mixing entropy and elastic energy if the volume of a long polymer is properly defined.