Genetic Network Programming (GNP) is an evolutionary computation which represents its solutions using graph structures. Since GNP can create quite compact programs and has an implicit memory function, it has been clarified that GNP works well especially in dynamic environments. In this paper, GNP is applied to creating a stock trading model. The first important point is to combine GNP with Actor-Critic which is one of the reinforcement learning algorithms. Evolution-based methods evolve their programs after task execution because they must calculate fitness values, while reinforcement learning can change programs during task execution, therefore the programs can be created efficiently. The second important point is that GNP with Actor-Critic (GNP-AC) can select appropriate technical indexes to judge the buying and selling timing of stocks using Importance Index especially designed for stock trading decision making. In the simulations, the trading model is trained using the stock prices of 20 brands in 2001, 2002 and 2003. Then the generalization ability is tested using the stock prices in 2004. From the simulation results, it is clarified that the trading rules of GNP-AC obtain higher profits than Buy&Hold method.