The stability of delayed Markovian generalized neural networks is studied where the transition rates of the modes are partly unknown. The partly unknown transition rates generalize the traditional works that are with all known transition rates. Then, a Lyapunov-Krasovskii functional (LKF) with a delay-product-type (DPT) term is constructed. The DPT term is not only simple but also fully utilizes the information of time delay. Based on the new DPT LKF, stability criteria are presented, which are with lower computational complexity and less conservative. In the end, the validity and superiorities of the analytical results are verified by several examples.