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The folding of a model protein confined in a nano-sized cylinder is studied by the off-lattice G-olike model. The entropy and anisotropy effects of confinement on thermodynamics and dynamics for folding are investigated. Our results show that due to reduction of the search on conformations, the folding rate can be sped up and the thermodynamic stability is enhanced at the cost of the decrease of folding cooperativity. In addition, it is found that these are shape-dependent. Folding is optimized in a cylinder with an appropriate shape when the volume is fixed. This is probably related to the shape of the protein molecule. Furthermore, our results also suggest that there is an orientational transition for the protein molecule following the variation of the radius of cylinder.