The mobile Ad Hoc network (MANET) is a self-organizing and self-configuring wireless network, consisting of a set of mobile nodes. The design of efficient routing protocols for MANET has always been an active area of research. In existing routing algorithms, however, the current work does not scale well enough to ensure route stability when the mobility and distribution of nodes vary with time. In addition, each node in MANET has only limited initial energy, so energy conservation and balance must be taken into account. An efficient routing algorithm should not only be stable but also energy saving and balanced, within the dynamic network environment. To address the above problems, we propose a stable and energy-efficient routing algorithm, based on learning automata (LA) theory for MANET. First, we construct a new node stability measurement model and define an effective energy ratio function. On that basis, we give the node a weighted value, which is used as the iteration parameter for LA. Next, we construct an LA theory-based feedback mechanism for the MANET environment to optimize the selection of available routes and to prove the convergence of our algorithm. The experiments show that our proposed LA-based routing algorithm for MANET achieved the best performance in route survival time, energy consumption, energy balance, and acceptable performance in end-to-end delay and packet delivery ratio.