In the paper authors describe proposition of design and verification procedures of the discrete Fractional Order PID (FOPID) algorithm for control of the Pressurized Water Reactor (PWR) thermal power near its nominal operating point. The FOPID algorithm synthesis consists of: off-line optimal tunning of its parameters in continuous time-domain with LQ (Linear Quadratic) performance index and simplified models of nuclear reactor and control rods drive; its transformation into equivalent integer order structure with Oustaloup filters; and finally its transformation into equivalent discrete form. Discrete FOPID algorithm is further implemented in the PLC controller and verified by real-time simulation in the Hardware In the Loop (HIL) structure with non-linear nuclear reactor model. Promising simulation results were obtained, which confirm improved flexibility of the discrete FOPID algorithm in comparison to its classical PID counterpart.