A simple core control code, SCLOF (Simple Core Control Code in Load Following Operation) is developed for the control of a nuclear reactor. The core state equations are described by the one-group diffusion equation with moderator temperature and xenon feedbacks and iodine-xenon dynamics equations. The control via control rod, boron, and coolant inlet temperature is considered. The control model is formulated as an optimal tracking problem with quadratic objective functional. An optimal solution is obtained by minimizing a quadratic functional of the power distribution and control effort. In order to avoid the conventional difficulties of two point boundary value problem, the optimal control problem is solved by the direct numerical technique of mathematical programming without the separation of space and time variables. This quadratic programming problem is solved by the Davidon-Fletcher-Powell(DFP) method which is a general unconstrained optimization method. By considering one time step optimization, optimal solutions are obtained with a minimum amount of computing time. In the cases of the load following operation of Korea Nuclear Unit 7 \& 8, the results obtained by using the present model show that the scheduled load demand is successfully followed and power distribution maintains the desired distribution with a minimum amount of control action.