We investigated the folding transition between an elongated coil state and a compact state on a single polymer chain confined in a small space with different stiffness with the aid of Monte Carlo simulation. In a flexible polymer, the folding transition is retarded in a confined space. In contrast, the transition is promoted for a semiflexible chain, in which the discontinuity of the volume change occupied by a single chain is diminished by confinement. This unique confinement effect is interpreted in terms of conformational entropy and self-avoiding repulsive interaction.