This paper presents a formulation of security-constrained unit commitment (SCUC) problem based on mixed integer programming (MIP) method with considering prohibited operating zone limits of thermal and hydro units. The objective of SCUC problem is to obtain minimum system operating cost while maintaining the system security. Thermal and hydro units in power system studies are assumed to possess smooth and convex input-output (IO) curves. Practically, not all the operating zones of generation units are available for load allocation due to some physical operation limits. This may cause to have a generator with nonsmooth IO curve with equality and inequality constraints which may not be solved easily by conventional mathematical methods. In this paper, non-convex characteristic of generator cost function, representing prohibited operating zones is considered in SCUC. Test results with an eight-bus system show the accuracy of the model and formulations.