In vitro, kinetically significant non-native interactions have been identified experimentally during the folding of proteins Im7, Im9, and A39V/N53P/VSSL Fyn SH3 domain. To understand the role of non-native interactions on the folding of some frustrated proteins in chaperone, we employed native-centric models with and without additional transferable, sequence-dependent non-native hydrophobic interactions to comparatively study the folding behaviors of the three proteins confined in spherical cages. Under purely repulsive confinement, as a decrease of cavity size, the non-native interactions increase, especially in the unfolded state, enhancing the roughness of the folding energy landscape. As a result, the increase in native stability for the three proteins by the model incorporated non-native interactions (db + MJh phi model) is much smaller than that by the purely native-centric model (desolvation-barrier (db) model); the acceleration of folding simulated by the db + MJh phi model is much slower than that via the db model; in particular, the folding rate of Im7 decreases when reducing the cavity size under zero-denaturant condition. The repulsive confinement can also promote formation of specific non-native contacts in the transition state and favor more folding pathways passing through the misfolded state, leading to a higher population of the misfolded intermediate. In an attractive cage, the attractive interactions could inhibit the formation of intrachain non-native contacts and provide alternate folding pathways to the native state so that the population of the misfolded intermediate decreases when increasing the strength of attractive interaction between the substrate protein and cavity wall. This study should be helpful in general to understand how the chaperonins reshape the folding energy landscape of some frustrated proteins.