Feature representation is critical not only for pattern recognition tasks but also for reinforcement learning (RL) methods to solve learning control problems under uncertainties. In this paper, a manifold-based RL approach using the principle of locally linear reconstruction (LLR) is proposed for Markov decision processes with large or continuous state spaces. In the proposed approach, an LLR-based feature learning scheme is developed for value function approximation in RL, where a set of smooth feature vectors is generated by preserving the local approximation properties of neighboring points in the original state space. By using the proposed feature learning scheme, an LLR-based approximate policy iteration (API) algorithm is designed for learning control problems with large or continuous state spaces. The relationship between the value approximation error of a new data point and the estimated values of its nearest neighbors is analyzed. In order to compare different feature representation and learning approaches for RL, a comprehensive simulation and experimental study was conducted on three benchmark learning control problems. It is illustrated that under a wide range of parameter settings, the LLR-based API algorithm can obtain better learning control performance than the previous API methods with different feature representation schemes.