In this work, extensive lattice Monte Carlo simulations were performed to investigate the influence of confinement on critical micelle concentration (CMC). It is found that the CMC of surfactants in a confined space is shifted from its bulk value, and the shift is affected by the presence of the confining boundaries, which induces both the finite size effect and the wall-surfactant interaction. In general, for strongly confined system (the system with narrow pore size), the finite size effect dominates the CMC shift because the confined space cannot accommodate fully developed micelles, and the rapid increase of the entropic loss due to the decrease of the pore size results in the rapid increase of CMC. In contrast, for a weakly confined space, the CMC shift depends on the interaction between the walls and surfactants. For the systems with two weakly hydrophilic surfaces, the local density depletion of the surfactants near the walls results in lower CMCs than the bulk value, and the CMC shifts to a higher value as the pore size increases. For the systems with moderately hydrophilic surfaces, the shifts of CMCs show a similar behavior as those for weakly hydrophilic surfaces, but the CMCs are near their bulk values in the range of weak confinement. For the systems with strongly attractive wall-surfactant interactions, the strong adsorption also results in lower CMCs than their bulk value, but the CMCs decrease with the increase of pore size.