The operation of Pumped Storage Hydro (PSH) units has great influence on the compilation of generation scheduling of power grid, a security constrained unit commitment model of power grid with PSH units is established. In the model, total operation cost of all units which includes the start up / stop down cost of PSH units is considered as the objective function, an analytical expression of the spinning reserve capacity of PSH units is given according to different operation conditions, and the network loss is considered in the power balance constraint of the system, the operation scheduling constraints of PSH units and the network security constraints are also considered. In order to ensure the reliability and improve the calculation efficiency of model solution, the objective function is piecewise linearized and the spinning reserve capacity constraint of PSH units is equivalently transformed into a linear expression according to their operation characteristics. Meanwhile, a dynamic piecewise linearization method is adopted to approximate the network loss, so that the unit commitment model is transformed into a Mixed Integer Linear Programming (MILP) model, which can be solved by using the mature mathematical optimization solver CPLEX. Test results on an actual power grid of 23 units and 306 buses demonstrate that the approximation effect of network loss in the proposed MILP model is reasonable and correct, and the proposed algorithm is fast and has good practical value in engineering. This work is supported by National Basic Research Program of China (973 Program) (No. 2013CB228205), Natural Science Foundation of Guangdong Province (No. 2015A030313233), and Science and Technology Project of Shenzhen Power Supply Bureau Co., Ltd (SZKJXM20160174).