This paper presents a coarse coding technique and an action selection scheme for reinforcement learning (RL) in multi-dimensional and continuous state-action spaces following conventional and sound RL manners. RL in high-dimensional continuous domains includes two issues: One is a generalization problem for value-function approximation, and the other is a sampling problem for action selection over multi-dimensional continuous action spaces. The proposed method combines random rectangular coarse coding with an action selection scheme using Gibbs-sampling. The random rectangular coarse coding is very simple and quite suited both to approximate Q-functions in high-dimensional spaces and to execute Gibbs sampling. Gibbs sampling enables us to execute action selection following Boltsmann distribution over high-dimensional action space. The algorithm is demonstrated through Rod in maze problem and a redundant-arm reaching task comparing with conventional regular grid approaches.